Celebratio Mathematica

Thomas Milton Liggett

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T. M. Lig­gett: “An in­vari­ance prin­ciple for con­di­tioned sums of in­de­pend­ent ran­dom vari­ables,” J. Math. Mech. 18 : 6 (1968), pp. 559–​570. MR 238373 Zbl 0181.​20502 article

T. M. Lig­gett and S. A. Lipp­man: “Stochast­ic games with per­fect in­form­a­tion and time av­er­age pay­off,” SIAM Rev. 11 : 4 (1969), pp. 604–​607. MR 260435 Zbl 0193.​19602 article

T. M. Lig­gett: Weak con­ver­gence of con­di­tioned sums of in­de­pend­ent ran­dom vec­tors. Ph.D. thesis, Stan­ford Uni­versity, 1969. Ad­vised by S. Karlin. An art­icle based on this was pub­lished in Trans. Am. Math. Soc. 152:1 (1970). MR 2618611 phdthesis

T. M. Lig­gett: “Con­ver­gence of sums of ran­dom vari­ables con­di­tioned on a fu­ture change of sign,” Ann. Math. Stat. 41 : 6 (1970), pp. 1978–​1982. MR 267630 Zbl 0219.​60021 article

T. M. Lig­gett: “Weak con­ver­gence of con­di­tioned sums of in­de­pend­ent ran­dom vec­tors,” Trans. Am. Math. Soc. 152 : 1 (November 1970), pp. 195–​213. Based on the au­thor’s 1969 PhD thes­is. MR 268940 Zbl 0221.​60018 article

T. M. Lig­gett: “On con­ver­gent dif­fu­sions: The dens­it­ies and the con­di­tioned pro­cesses,” In­di­ana Univ. Math. J. 20 : 3 (1970–1971), pp. 265–​279. MR 272062 Zbl 0181.​44302 article

M. G. Cran­dall and T. M. Lig­gett: “Gen­er­a­tion of semi-groups of non­lin­ear trans­form­a­tions on gen­er­al Banach spaces,” Am. J. Math. 93 : 2 (April 1971), pp. 265–​298. MR 287357 Zbl 0226.​47038 article

M. G. Cran­dall and T. M. Lig­gett: “A the­or­em and a counter­example in the the­ory of semig­roups of non­lin­ear trans­form­a­tions,” Trans. Am. Math. Soc. 160 (October 1971), pp. 263–​278. MR 301592 Zbl 0226.​47037 article

T. M. Lig­gett: “Ex­ist­ence the­or­ems for in­fin­ite particle sys­tems,” Trans. Am. Math. Soc. 165 (1972), pp. 471–​481. MR 309218 Zbl 0239.​60072 article

D. A. Darling, T. Lig­gett, and H. M. Taylor: “Op­tim­al stop­ping for par­tial sums,” Ann. Math. Stat. 43 : 4 (1972), pp. 1363–​1368. MR 312564 Zbl 0244.​60037 article

T. M. Lig­gett: “A char­ac­ter­iz­a­tion of the in­vari­ant meas­ures for an in­fin­ite particle sys­tem with in­ter­ac­tions,” Trans. Am. Math. Soc. 179 (1973), pp. 433–​453. MR 326867 Zbl 0268.​60090 article

T. M. Lig­gett: “An in­fin­ite particle sys­tem with zero range in­ter­ac­tions,” Ann. Probab. 1 : 2 (1973), pp. 240–​253. MR 381039 Zbl 0264.​60083 article

T. M. Lig­gett: “Con­ver­gence to total oc­cu­pancy in an in­fin­ite particle sys­tem with in­ter­ac­tions,” Ann. Probab. 2 : 6 (1974), pp. 989–​998. MR 362564 Zbl 0295.​60086 article

T. M. Lig­gett: “A char­ac­ter­iz­a­tion of the in­vari­ant meas­ures for an in­fin­ite particle sys­tem with in­ter­ac­tions, II,” Trans. Am. Math. Soc. 198 (1974), pp. 201–​213. MR 375531 Zbl 0364.​60118 article

R. A. Hol­ley and T. M. Lig­gett: “Er­god­ic the­or­ems for weakly in­ter­act­ing in­fin­ite sys­tems and the voter mod­el,” Ann. Probab. 3 : 4 (1975), pp. 643–​663. MR 402985 Zbl 0367.​60115 article

T. M. Lig­gett: “Er­god­ic the­or­ems for the asym­met­ric simple ex­clu­sion pro­cess,” Trans. Am. Math. Soc. 213 (1975), pp. 237–​261. Part II was pub­lished in Ann. Probab 5:5 (1977). MR 410986 Zbl 0322.​60086 article

T. M. Lig­gett: “Coup­ling the simple ex­clu­sion pro­cess,” Ann. Probab. 4 : 3 (1976), pp. 339–​356. MR 418291 Zbl 0339.​60091 article

T. M. Lig­gett: “Ex­ten­sions of the Er­dős–Ko–Rado the­or­em and a stat­ist­ic­al ap­plic­a­tion,” J. Comb. The­ory, Ser. A 23 : 1 (July 1977), pp. 15–​21. MR 441750 Zbl 0361.​05011 article

J. Hoff­mann-Jør­gensen, T. M. Lig­gett, and J. Neveu: École d’été de prob­ab­ilités Saint-Flour VI [6th Saint-Flour sum­mer school on prob­ab­il­ity] (Saint-Flour, France, 22 Au­gust–8 Septem­ber 1976). Edi­ted by P.-L. Hen­nequin. Lec­ture Notes in Math­em­at­ics 598. Spring­er (Ber­lin), 1977. Lig­gett’s con­tri­bu­tion was re­pub­lished in In­ter­act­ing particle sys­tems at Saint-Flour (2012). MR 443008 Zbl 0348.​00009 book

T. M. Lig­gett: “Er­god­ic the­or­ems for the asym­met­ric simple ex­clu­sion pro­cess, II,” Ann. Probab. 5 : 5 (1977), pp. 795–​801. Part I was pub­lished in Trans. Am. Math. Soc. 213 (1975). MR 445644 Zbl 0378.​60104 article

T. M. Lig­gett: “The stochast­ic evol­u­tion of in­fin­ite sys­tems of in­ter­act­ing particles,” pp. 187–​248 in J. Hoff­mann-Jør­gensen, T. M. Lig­gett, and J. Neveu: École d’été de prob­ab­ilités Saint-Flour VI [6th Saint-Flour sum­mer school on prob­ab­il­ity] (Saint-Flour, France, 22 Au­gust–8 Septem­ber 1976). Edi­ted by P.-L. Hen­nequin. Lec­ture Notes in Math­em­at­ics 598. Spring­er (Ber­lin), 1977. MR 458647 Zbl 0363.​60109 incollection

R. Hol­ley and T. M. Lig­gett: “The sur­viv­al of con­tact pro­cesses,” Ann. Probab. 6 : 2 (1978), pp. 198–​206. MR 488379 Zbl 0375.​60111 article

T. M. Lig­gett: “At­tract­ive nearest neigh­bor spin sys­tems on the in­tegers,” Ann. Probab. 6 : 4 (1978), pp. 629–​636. MR 494569 Zbl 0381.​60095 article

T. M. Lig­gett: “Ran­dom in­vari­ant meas­ures for Markov chains and in­de­pend­ent particle sys­tems,” Z. Wahr­schein­lich­keit­s­the­or. Verw. Geb. 45 : 4 (1978), pp. 297–​313. MR 511776 Zbl 0373.​60076 article

T. M. Lig­gett: “Long range ex­clu­sion pro­cesses,” Ann. Probab. 8 : 5 (1980), pp. 861–​889. MR 586773 Zbl 0457.​60079 article

T. M. Lig­gett: “In­ter­act­ing Markov pro­cesses,” pp. 145–​156 in Bio­lo­gic­al growth and spread: Math­em­at­ic­al the­or­ies and ap­plic­a­tions (Heidel­berg, Ger­many, 16–21 Ju­ly 1979). Edi­ted by W. Jäger, H. Rost, and P. Tăutu. Lec­ture Notes in Bio­mathem­at­ics 38. Spring­er (Ber­lin), 1980. MR 609355 Zbl 0457.​60080 incollection

R. Dur­rett and T. M. Lig­gett: “The shape of the lim­it set in Richard­son’s growth mod­el,” Ann. Probab. 9 : 2 (1981), pp. 186–​193. MR 606981 Zbl 0457.​60083 article

R. Hol­ley and T. M. Lig­gett: “Gen­er­al­ized pot­latch and smooth­ing pro­cesses,” Z. Wahr­schein­lich­keit­s­the­or. Verw. Geb. 55 : 2 (1981), pp. 165–​195. MR 608015 Zbl 0441.​60096 article

T. M. Lig­gett and F. Spitzer: “Er­god­ic the­or­ems for coupled ran­dom walks and oth­er sys­tems with loc­ally in­ter­act­ing com­pon­ents,” Z. Wahr­schein­lich­keit­s­the­or. Verw. Geb. 56 (1981), pp. 443–​468. MR 621659 Zbl 0444.​60096 article

D. Grif­feath and T. M. Lig­gett: “Crit­ic­al phe­nom­ena for Spitzer’s re­vers­ible nearest particle sys­tems,” Ann. Probab. 10 : 4 (1982), pp. 881–​895. MR 672290 Zbl 0498.​60090 article

T. M. Lig­gett: “At­tract­ive nearest particle sys­tems,” Ann. Probab. 11 : 1 (1983), pp. 16–​33. MR 682797 Zbl 0508.​60081 article

T. M. Lig­gett: “Two crit­ic­al ex­po­nents for fi­nite re­vers­ible nearest particle sys­tems,” Ann. Probab. 11 : 3 (1983), pp. 714–​725. MR 704558 Zbl 0527.​60093 article

R. Dur­rett and T. M. Lig­gett: “Fixed points of the smooth­ing trans­form­a­tion,” Z. Wahr­schein­lich­keit­s­the­or. Verw. Geb. 64 : 3 (1983), pp. 275–​301. MR 716487 Zbl 0506.​60097 article

T. M. Lig­gett: “Fi­nite nearest particle sys­tems,” Z. Wahr­schein­lich­keit­s­the­or. Verw. Geb. 68 : 1 (1984), pp. 65–​73. MR 767445 Zbl 0557.​60087 article

T. M. Lig­gett: In­ter­act­ing particle sys­tems. Grundlehren der Math­em­at­ischen Wis­senschaften 276. Spring­er (New York), 1985. Re­prin­ted in 2005. A Rus­si­an trans­la­tion was pub­lished as Markovskie prot­sessy s lokal’nym vzaimod­ejstviem (1989). MR 776231 Zbl 0559.​60078 book

T. M. Lig­gett: “An im­proved sub­ad­dit­ive er­god­ic the­or­em,” Ann. Probab. 13 : 4 (1985), pp. 1279–​1285. MR 806224 Zbl 0579.​60023 article

T. M. Lig­gett: “Nearest particle sys­tems: Res­ults and open prob­lems,” pp. 200–​215 in Stochast­ic spa­tial pro­cesses: Math­em­at­ic­al the­or­ies and bio­lo­gic­al ap­plic­a­tions (Heidel­berg, Ger­many, 10–14 Septem­ber 1984). Edi­ted by P. Tautu. Lec­ture Notes in Math­em­at­ics 1212. Spring­er (Ber­lin), 1986. MR 877777 Zbl 0603.​60094 incollection

T. M. Lig­gett: “Ap­plic­a­tions of the Di­rich­let prin­ciple to fi­nite re­vers­ible nearest particle sys­tems,” Probab. The­ory Re­lat. Fields 74 : 4 (1987), pp. 505–​528. MR 876253 Zbl 0589.​60081 article

T. M. Lig­gett: “Re­vers­ible growth mod­els on \( \mathbb{Z}^d \): Some ex­amples,” pp. 213–​227 in Per­col­a­tion the­ory and er­god­ic the­ory of in­fin­ite particle sys­tems (Min­neapol­is, MN, 1984–1985). Edi­ted by H. Kesten. IMA Volumes in Math­em­at­ics and its Ap­plic­a­tions 8. Spring­er (New York), 1987. MR 894550 Zbl 0636.​60104 incollection

T. M. Lig­gett: “Re­vers­ible growth mod­els on sym­met­ric sets,” pp. 275–​301 in Prob­ab­il­ist­ic meth­ods in math­em­at­ic­al phys­ics (Kata­ta and Kyoto, Ja­pan, 20–26 June 1985). Edi­ted by K. Itô and N. Ike­da. Aca­dem­ic Press (Bo­ston), 1987. MR 933828 Zbl 0653.​60094 incollection

T. M. Lig­gett: “Spa­tial stochast­ic growth mod­els–sur­viv­al and crit­ic­al be­ha­vi­or,” pp. 1032–​1041 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Berke­ley, CA, 3–11 Au­gust 1986), vol. 2. Edi­ted by A. M. Gleason. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1987. MR 934305 Zbl 0667.​92012 incollection

T. M. Lig­gett and S. C. Port: “Sys­tems of in­de­pend­ent Markov chains,” Stochast­ic Pro­cesses Ap­pl. 28 : 1 (1988), pp. 1–​22. MR 936369 Zbl 0657.​60123 article

E. D. An­djel, M. D. Bramson, and T. M. Lig­gett: “Shocks in the asym­met­ric ex­clu­sion pro­cess,” Probab. The­ory Re­lat. Fields 78 : 2 (June 1988), pp. 231–​247. MR 945111 Zbl 0632.​60107 article

T. Lig­gett: Markovskie prot­sessy s lokal’nym vzaimod­ejstviem [Markov pro­cesses with loc­al in­ter­ac­tion]. Mir (Mo­scow), 1989. Ed­ited and with a pre­face by R. L. Dobrush­in. Rus­si­an trans­la­tion of In­ter­act­ing particle sys­tems (1985),. MR 993073 Zbl 0741.​60102 book

T. M. Lig­gett: “Total pos­it­iv­ity and re­new­al the­ory,” pp. 141–​162 in Prob­ab­il­ity, stat­ist­ics, and math­em­at­ics: Pa­pers in hon­or of Samuel Karlin. Edi­ted by T. W. An­der­son, K. B. Ath­reya, and D. L. Ig­le­hart. Aca­dem­ic Press (Bo­ston), 1989. MR 1031283 Zbl 0682.​60078 incollection

T. M. Lig­gett: “Ex­po­nen­tial \( L_2 \) con­ver­gence of at­tract­ive re­vers­ible nearest particle sys­tems,” Ann. Probab. 17 : 2 (1989), pp. 403–​432. MR 985371 Zbl 0679.​60093 article

W.-D. Ding, R. Dur­rett, and T. M. Lig­gett: “Er­godi­city of re­vers­ible re­ac­tion dif­fu­sion pro­cesses,” Probab. The­ory Re­lat. Fields 85 : 1 (March 1990), pp. 13–​26. MR 1044295 Zbl 0669.​60077 article

T. M. Lig­gett: “\( L_2 \) rates of con­ver­gence for at­tract­ive re­vers­ible nearest particle sys­tems: The crit­ic­al case,” Ann. Probab. 19 : 3 (July 1991), pp. 935–​959. MR 1112402 Zbl 0737.​60092 article

T. M. Lig­gett: “Lim­it­ing be­ha­vi­or of a one-di­men­sion­al sys­tem with long range in­ter­ac­tions,” pp. 31–​40 in Math­em­at­ics of ran­dom me­dia (Blacks­burg, VA, 29 May–9 June 1989). Edi­ted by W. E. Kohler and B. S. White. Lec­tures in Ap­plied Math­em­at­ics 27. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1991. MR 1117234 Zbl 0731.​60094 incollection

T. M. Lig­gett: “Spa­tially in­homo­gen­eous con­tact pro­cesses,” pp. 105–​140 in Spa­tial stochast­ic pro­cesses. Edi­ted by K. S. Al­ex­an­der and J. C. Watkins. Pro­gress in Prob­ab­il­ity 19. Birkäuser (Bo­ston), 1991. A Fest­s­chrift in hon­or of Ted Har­ris on his sev­en­ti­eth birth­day. MR 1144094 Zbl 0747.​60096 incollection

T. M. Lig­gett: “The peri­od­ic threshold con­tact pro­cess,” pp. 339–​358 in Ran­dom walks, Browni­an mo­tion, and in­ter­act­ing particle sys­tems. Edi­ted by R. Dur­rett and H. Kesten. Pro­gress in Prob­ab­il­ity 28. Birkhäuser (Bo­ston), 1991. A Fest­s­chrift in hon­or of Frank Spitzer. MR 1146457 Zbl 0747.​60097 incollection

T. M. Lig­gett: “The sur­viv­al of one-di­men­sion­al con­tact pro­cesses in ran­dom en­vir­on­ments,” Ann. Probab. 20 : 2 (1992), pp. 696–​723. MR 1159569 Zbl 0754.​60126 article

J. E. Co­hen and T. M. Lig­gett: “Ran­dom arith­met­ic-geo­met­ric means and ran­dom pi: Ob­ser­va­tions and con­jec­tures,” Stochast­ic Pro­cesses Ap­pl. 41 : 2 (June 1992), pp. 261–​271. MR 1164179 Zbl 0756.​60056 article

E. D. An­djel, T. M. Lig­gett, and T. Mount­ford: “Clus­ter­ing in one-di­men­sion­al threshold voter mod­els,” Stochast­ic Pro­cesses Ap­pl. 42 : 1 (August 1992), pp. 73–​90. MR 1172508 Zbl 0752.​60086 article

D. Chen and T. M. Lig­gett: “Fi­nite re­vers­ible nearest particle sys­tems in in­homo­gen­eous and ran­dom en­vir­on­ments,” Ann. Probab. 20 : 1 (January 1992), pp. 152–​173. MR 1143416 Zbl 0753.​60099 article

T. M. Lig­gett: “The coup­ling tech­nique in in­ter­act­ing particle sys­tems,” pp. 73–​83 in Doeblin and mod­ern prob­ab­il­ity (Blaubeuren, Ger­many, 2–7 Novem­ber 1991). Edi­ted by H. Cohn. Con­tem­por­ary Math­em­at­ics 149. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1993. MR 1229954 Zbl 0796.​60099 incollection

T. M. Lig­gett: “Clus­ter­ing and co­ex­ist­ence in threshold voter mod­els,” pp. 403–​410 in Cel­lu­lar auto­mata and co­oper­at­ive sys­tems (Les Houches, France, 22 June–2 Ju­ly 1992). Edi­ted by N. Boc­cara, E. Goles, S. Martínez, and P. Picco. NATO Sci­ence Series C: Math­em­at­ic­al and Phys­ic­al Sci­ences 396. Kluwer Aca­dem­ic (Dordrecht), 1993. MR 1267982 Zbl 0869.​60086 incollection

T. M. Lig­gett: “Sur­viv­al and co­ex­ist­ence in in­ter­act­ing particle sys­tems,” pp. 209–​226 in Prob­ab­il­ity and phase trans­ition (Cam­bridge, UK, 4–16 Ju­ly 1993). Edi­ted by G. Grim­mett. NATO Sci­ence Series C: Math­em­at­ic­al and Phys­ic­al Sci­ences 420. Kluwer Aca­dem­ic (Dordrecht), 1994. MR 1283183 Zbl 0832.​60094 incollection

J. Aaron­son, T. Lig­gett, and P. Picco: “Equi­val­ence of re­new­al se­quences and iso­morph­ism of ran­dom walks,” Isr. J. Math. 87 : 1–​3 (1994), pp. 65–​76. MR 1286815 Zbl 0808.​60063 article

G. A. Kriegs­mann, K. L. Lange, and T. M. Lig­gett: “Charles G. Lange (March 30, 1942–June 25, 1993),” Meth­ods Ap­pl. Anal. 1 : 4 (1994), pp. 387–​391. MR 1317018 Zbl 0832.​01014 article

T. M. Lig­gett and P. Petersen: “The law of large num­bers and \( \sqrt{2} \),” Am. Math. Monthly 102 : 1 (January 1995), pp. 31–​35. MR 1321453 Zbl 0823.​60023 article

T. M. Lig­gett: “Im­proved up­per bounds for the con­tact pro­cess crit­ic­al value,” Ann. Probab. 23 : 2 (1995), pp. 697–​723. MR 1334167 Zbl 0832.​60093 article

P. A. Fer­rari, A. Galves, and T. M. Lig­gett: “Ex­po­nen­tial wait­ing time for filling a large in­ter­val in the sym­met­ric simple ex­clu­sion pro­cess,” Ann. Inst. H. Poin­caré Probab. Stat­ist. 31 : 1 (1995), pp. 155–​175. With French ab­stract. MR 1340035 Zbl 0819.​60095 article

T. M. Lig­gett: “Sur­viv­al of dis­crete time growth mod­els, with ap­plic­a­tions to ori­ented per­col­a­tion,” Ann. Ap­pl. Probab. 5 : 3 (1995), pp. 613–​636. MR 1359822 Zbl 0842.​60090 article

T. M. Lig­gett: “Mul­tiple trans­ition points for the con­tact pro­cess on the bin­ary tree,” Ann. Probab. 24 : 4 (1996), pp. 1675–​1710. MR 1415225 Zbl 0871.​60087 article

T. M. Lig­gett: “Branch­ing ran­dom walks and con­tact pro­cesses on ho­mo­gen­eous trees,” Probab. The­ory Re­lated Fields 106 : 4 (1996), pp. 495–​519. MR 1421990 Zbl 0867.​60092 article

T. M. Lig­gett: “Stochast­ic mod­els of in­ter­act­ing sys­tems,” Ann. Probab. 25 : 1 (1997), pp. 1–​29. From the 1996 Wald Me­mori­al Lec­tures. MR 1428497 Zbl 0873.​60072 article

T. M. Lig­gett, R. H. Schon­mann, and A. M. Sta­cey: “Dom­in­a­tion by product meas­ures,” Ann. Probab. 25 : 1 (1997), pp. 71–​95. MR 1428500 Zbl 0882.​60046 article

V. Be­l­it­sky, P. A. Fer­rari, N. Konno, and T. M. Lig­gett: “A strong cor­rel­a­tion in­equal­ity for con­tact pro­cesses and ori­ented per­col­a­tion,” Stochast­ic Pro­cess. Ap­pl. 67 : 2 (1997), pp. 213–​225. MR 1449832 Zbl 0890.​60094 article

T. M. Lig­gett: “Ul­tra lo­g­con­cave se­quences and neg­at­ive de­pend­ence,” J. Com­bin. The­ory Ser. A 79 : 2 (August 1997), pp. 315–​325. MR 1462561 Zbl 0888.​60013 article

T. M. Lig­gett: “Cor­rec­tion: ‘Co­ex­ist­ence in threshold voter mod­els’,” Ann. Probab. 27 : 4 (1999), pp. 2120–​2121. Cor­rec­tion to an art­icle pub­lished in Ann. Probab. 22:2 (1994). MR 1742905 Zbl 0814.​60094 article

T. M. Lig­gett: “Branch­ing ran­dom walks on fi­nite trees,” pp. 315–​330 in Per­plex­ing prob­lems in prob­ab­il­ity: Fest­s­chrift in hon­or of Harry Kesten. Edi­ted by M. Bramson and R. Dur­rett. Pro­gress in Prob­ab­il­ity 44. Birkhäuser (Bo­ston), 1999. MR 1703138 Zbl 0948.​60097 incollection

T. M. Lig­gett: Stochast­ic in­ter­act­ing sys­tems: Con­tact, voter and ex­clu­sion pro­cesses. Grundlehren der Math­em­at­ischen Wis­senschaften 324. Spring­er (Ber­lin), 1999. MR 1717346 Zbl 0949.​60006 book

T. M. Lig­gett: “Mono­ton­icity of con­di­tion­al dis­tri­bu­tions and growth mod­els on trees,” Ann. Probab. 28 : 4 (2000), pp. 1645–​1665. MR 1813837 Zbl 1044.​60094 article

A. E. Hol­royd and T. M. Lig­gett: “How to find an ex­tra head: Op­tim­al ran­dom shifts of Bernoulli and Pois­son ran­dom fields,” Ann. Probab. 29 : 4 (2001), pp. 1405–​1425. MR 1880225 Zbl 1019.​60048 article

T. M. Lig­gett: “Tagged particle dis­tri­bu­tions or how to choose a head at ran­dom,” pp. 133–​162 in In and out of equi­lib­ri­um: Prob­ab­il­ity with a phys­ics fla­vor (Mam­bu­caba, Brazil, 14–19 Au­gust 2000). Edi­ted by V. Sidoravi­cius. Pro­gress in Prob­ab­il­ity 51. Birkhäuser (Bo­ston), 2002. MR 1901951 Zbl 1108.​60319 incollection

M. Bramson, T. M. Lig­gett, and T. Mount­ford: “Char­ac­ter­iz­a­tion of sta­tion­ary meas­ures for one-di­men­sion­al ex­clu­sion pro­cesses,” Ann. Probab. 30 : 4 (2002), pp. 1539–​1575. MR 1944000 Zbl 1039.​60086 article

T. M. Lig­gett: “Neg­at­ive cor­rel­a­tions and particle sys­tems,” Markov Pro­cess. Re­lated Fields 8 : 4 (2002), pp. 547–​564. MR 1957219 Zbl 1021.​60084 article

P. Bonacich and T. M. Lig­gett: “Asymp­tot­ics of a mat­rix val­ued Markov chain arising in so­ci­ology,” Stochast­ic Pro­cess. Ap­pl. 104 : 1 (2003), pp. 155–​171. MR 1956477 Zbl 1075.​60546 article

A. E. Hol­royd, T. M. Lig­gett, and D. Romik: “In­teg­rals, par­ti­tions, and cel­lu­lar auto­mata,” Trans. Am. Math. Soc. 356 : 8 (2004), pp. 3349–​3368. MR 2052953 Zbl 1095.​60003 ArXiv math/​0302216 article

T. M. Lig­gett and S. W. W. Rolles: “An in­fin­ite stochast­ic mod­el of so­cial net­work form­a­tion,” Stochast­ic Pro­cess. Ap­pl. 113 : 1 (2004), pp. 65–​80. MR 2078537 Zbl 1071.​60097 article

T. M. Lig­gett: “In­ter­act­ing particle sys­tems — an in­tro­duc­tion,” pp. 1–​56 in School and con­fer­ence on prob­ab­il­ity the­ory (Trieste, Italy, 13–17 May 2002). Edi­ted by G. F. Lawl­er. ICTP Lec­ture Notes 17. Ab­dus Salam In­ter­na­tion­al Cen­ter for The­or­et­ic­al Phys­ics (Trieste), 2004. MR 2198846 Zbl 1221.​60141 incollection

T. M. Lig­gett: In­ter­act­ing particle sys­tems, Re­prin­ted edition. Clas­sics in Math­em­at­ics. Spring­er (New York), 2005. Re­print of the 1985 ori­gin­al. MR 2108619 Zbl 1103.​82016 book

R. Ar­ra­tia and T. M. Lig­gett: “How likely is an i.i.d. de­gree se­quence to be graph­ic­al?,” Ann. Ap­pl. Probab. 15 : 1B (2005), pp. 652–​670. MR 2114985 Zbl 1079.​05023 ArXiv math/​0504096 article

M. Bramson and T. M. Lig­gett: “Ex­clu­sion pro­cesses in high­er di­men­sions: Sta­tion­ary meas­ures and con­ver­gence,” Ann. Probab. 33 : 6 (2005), pp. 2255–​2313. MR 2184097 Zbl 1099.​60067 article

T. M. Lig­gett and J. E. Steif: “Stochast­ic dom­in­a­tion: The con­tact pro­cess, Ising mod­els and FKG meas­ures,” Ann. Inst. H. Poin­caré Probab. Stat­ist. 42 : 2 (March–April 2006), pp. 223–​243. MR 2199800 Zbl 1087.​60074 ArXiv math/​0504530 article

T. M. Lig­gett: “Con­di­tion­al as­so­ci­ation and spin sys­tems,” ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006), pp. 1–​19. MR 2235171 Zbl 1157.​60088 ArXiv math/​0507392 article

T. M. Lig­gett, J. E. Steif, and B. Tóth: “Stat­ist­ic­al mech­an­ic­al sys­tems on com­plete graphs, in­fin­ite ex­change­ab­il­ity, fi­nite ex­ten­sions and a dis­crete fi­nite mo­ment prob­lem,” Ann. Probab. 35 : 3 (2007), pp. 867–​914. MR 2319710 Zbl 1126.​44007 ArXiv math/​0512191 article

L. Chayes and T. M. Lig­gett: “One di­men­sion­al nearest neigh­bor ex­clu­sion pro­cesses in in­homo­gen­eous and ran­dom en­vir­on­ments,” J. Stat. Phys. 129 : 2 (2007), pp. 193–​203. MR 2358802 Zbl 1141.​82015 ArXiv math/​0701180 article

T. M. Lig­gett, R. B. Schinazi, and J. Sch­weins­berg: “A con­tact pro­cess with muta­tions on a tree,” Stochast­ic Pro­cess. Ap­pl. 118 : 3 (2008), pp. 319–​332. MR 2389047 Zbl 1141.​60065 ArXiv math/​0612564 article

J. Bor­cea, P. Brändén, and T. M. Lig­gett: “Neg­at­ive de­pend­ence and the geo­metry of poly­no­mi­als,” J. Am. Math. Soc. 22 : 2 (2009), pp. 521–​567. MR 2476782 Zbl 1206.​62096 ArXiv 0707.​2340 article

T. M. Lig­gett: “Dis­tri­bu­tion­al lim­its for the sym­met­ric ex­clu­sion pro­cess,” Stochast­ic Pro­cess. Ap­pl. 119 : 1 (January 2009), pp. 1–​15. MR 2485017 Zbl 1172.​60031 article

T. M. Lig­gett, S. A. Lipp­man, and R. P. Rumelt: “The asymp­tot­ic Shap­ley value for a simple mar­ket game,” Eco­nom. The­ory 40 : 2 (2009), pp. 333–​338. MR 2507870 Zbl 1173.​91372 article

T. M. Lig­gett and R. B. Schinazi: “A stochast­ic mod­el for phylo­gen­et­ic trees,” J. Ap­pl. Probab. 46 : 2 (June 2009), pp. 601–​607. MR 2535836 Zbl 1180.​60079 article

T. M. Lig­gett: Con­tinu­ous time Markov pro­cesses: An in­tro­duc­tion. Gradu­ate Stud­ies in Math­em­at­ics 113. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2010. MR 2574430 Zbl 1205.​60002 book

P. Cap­uto, T. M. Lig­gett, and T. Rich­tham­mer: “Proof of Al­dous’ spec­tral gap con­jec­ture,” J. Am. Math. Soc. 23 : 3 (2010), pp. 831–​851. MR 2629990 Zbl 1203.​60145 ArXiv 0906.​1238 article

G. R. Grim­mett, T. M. Lig­gett, and T. Rich­tham­mer: “Per­col­a­tion of ar­bit­rary words in one di­men­sion,” Ran­dom Struc­tures Al­gorithms 37 : 1 (2010), pp. 85–​99. MR 2674622 Zbl 1202.​60155 ArXiv 0807.​1676 article

T. M. Lig­gett: “Stochast­ic mod­els for large in­ter­act­ing sys­tems and re­lated cor­rel­a­tion in­equal­it­ies,” Proc. Natl. Acad. Sci. USA 107 : 38 (2010), pp. 16413–​16419. MR 2726545 Zbl 1256.​60037 article

T. M. Lig­gett: “T. E. Har­ris’ con­tri­bu­tions to in­ter­act­ing particle sys­tems and per­col­a­tion,” Ann. Probab. 39 : 2 (2011), pp. 407–​416. MR 2789500 Zbl 1213.​60159 ArXiv 1103.​1988 article

T. M. Lig­gett and A. Vanden­berg-Rodes: “Sta­bil­ity on \( \{0,1,2,\dots\}^S \): Birth-death chains and particle sys­tems,” pp. 311–​329 in No­tions of pos­it­iv­ity and the geo­metry of poly­no­mi­als: Ded­ic­ated to the memory of Ju­li­us Bor­cea. Edi­ted by P. Brändén, M. Pas­sare, and M. Putin­ar. Trends in Math­em­at­ics. Birkhäuser (Basel), 2011. MR 3051173 Zbl 1278.​60144 ArXiv 1009.​4899 incollection

R. Dur­rett, T. M. Lig­gett, F. Spitzer, and A.-S. Szn­it­man: In­ter­act­ing particle sys­tems at Saint-Flour (Saint-Flour, France, 1964–1993). Prob­ab­il­ity at Saint-Flour. Spring­er (Ber­lin), 2012. Re­print of vari­ous lec­tures ori­gin­ally pub­lished Lec­ture Notes in Math­em­at­ics 390 (1974), \xlink589 (1977)|MR:0443008, 1464 (1991) and 1608 (1995). MR 3075635 Zbl 1248.​82021 book

R. Dur­rett, T. Lig­gett, and Y. Zhang: “The con­tact pro­cess with fast vot­ing,” Elec­tron. J. Probab. 19 (2014), pp. Article no. 28, 19 pages. MR 3174840 Zbl 1291.​60203 article

R. Ar­ra­tia, T. M. Lig­gett, and M. J. Wil­li­am­son: “Scale-free and power law dis­tri­bu­tions via fixed points and con­ver­gence of (thin­ning and con­di­tion­ing) trans­form­a­tions,” Elec­tron. Com­mun. Probab. 19 (2014). Art­icle no. 39, 10 pages. MR 3225870 Zbl 1320.​60010 ArXiv 1306.​3017 article

A. E. Hol­royd and T. M. Lig­gett: “Sym­met­ric 1-de­pend­ent col­or­ings of the in­tegers,” Elec­tron. Com­mun. Probab. 20 (2015). Art­icle no. 31, 8 pages. MR 3327870 Zbl 1385.​60014 ArXiv 1407.​4514 article

A. E. Hol­royd and T. M. Lig­gett: “Fi­nitely de­pend­ent col­or­ing,” For­um Math. Pi 4 (2016). Art­icle no. e9, 43 pages; Ded­ic­ated to Oded Schramm. MR 3570073 Zbl 1361.​60025 ArXiv 1403.​2448 article

S. Ghosh, T. M. Lig­gett, and R. Pe­mantle: “Mul­tivari­ate CLT fol­lows from strong Rayleigh prop­erty,” pp. 139–​147 in 2017 pro­ceed­ings of the four­teenth work­shop on ana­lyt­ic al­gorithmics and com­bin­at­or­ics (ANALCO) (Bar­celona, 16–17 Janu­ary 2017). Edi­ted by C. Martínez and M. D. Ward. SIAM (Phil­adelphia, PA), 2017. MR 3630942 Zbl 1432.​60034 incollection

T. M. Lig­gett and W. Tang: One-de­pend­ent col­or­ings of the star graph. Pre­print, April 2018. ArXiv 1804.​06877 techreport

T. M. Lig­gett: “Ap­prox­im­at­ing mul­tiples of strong Rayleigh ran­dom vari­ables,” Cel­eb­ra­tio Math­em­at­ica (2021). article