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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

: “Stochastic games with perfect information and time average payoff,” SIAM Rev. 11 : 4 (1969), pp. 604–607. MR 260435 Zbl 0193.19602 article

: “
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

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

: “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

: “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

: “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

: “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

: “Existence theorems for infinite particle systems,” Trans. Am. Math. Soc. 165 (1972), pp. 471–481. MR 309218 Zbl 0239.60072 article

: “Optimal stopping for partial sums,” Ann. Math. Stat. 43 : 4 (1972), pp. 1363–1368. MR 312564 Zbl 0244.60037 article

: “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

: “An infinite particle system with zero range interactions,” Ann. Probab. 1 : 2 (1973), pp. 240–253. MR 381039 Zbl 0264.60083 article

: “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

: “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

: “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

: “
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

Coupling the simple exclusion process,” Ann. Probab. 4 : 3 (1976), pp. 339–356. MR 418291 Zbl 0339.60091 article

: “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

: “
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

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

The stochastic evolution of infinite systems of interacting particles,” pp. 187–248 in : 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

: “The survival of contact processes,” Ann. Probab. 6 : 2 (1978), pp. 198–206. MR 488379 Zbl 0375.60111 article

: “Attractive nearest neighbor spin systems on the integers,” Ann. Probab. 6 : 4 (1978), pp. 629–636. MR 494569 Zbl 0381.60095 article

: “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

: “Long range exclusion processes,” Ann. Probab. 8 : 5 (1980), pp. 861–889. MR 586773 Zbl 0457.60079 article

: “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

: “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

: “Generalized potlatch and smoothing processes,” Z. Wahrscheinlichkeitstheor. Verw. Geb. 55 : 2 (1981), pp. 165–195. MR 608015 Zbl 0441.60096 article

: “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

: “Critical phenomena for Spitzer’s reversible nearest particle systems,” Ann. Probab. 10 : 4 (1982), pp. 881–895. MR 672290 Zbl 0498.60090 article

: “Attractive nearest particle systems,” Ann. Probab. 11 : 1 (1983), pp. 16–33. MR 682797 Zbl 0508.60081 article

: “Two critical exponents for finite reversible nearest particle systems,” Ann. Probab. 11 : 3 (1983), pp. 714–725. MR 704558 Zbl 0527.60093 article

: “Fixed points of the smoothing transformation,” Z. Wahrscheinlichkeitstheor. Verw. Geb. 64 : 3 (1983), pp. 275–301. MR 716487 Zbl 0506.60097 article

: “Finite nearest particle systems,” Z. Wahrscheinlichkeitstheor. Verw. Geb. 68 : 1 (1984), pp. 65–73. MR 767445 Zbl 0557.60087 article

: “
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

An improved subadditive ergodic theorem,” Ann. Probab. 13 : 4 (1985), pp. 1279–1285. MR 806224 Zbl 0579.60023 article

: “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

: “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

: “
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

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

: “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

: “Systems of independent Markov chains,” Stochastic Processes Appl. 28 : 1 (1988), pp. 1–22. MR 936369 Zbl 0657.60123 article

: “Shocks in the asymmetric exclusion process,” Probab. Theory Relat. Fields 78 : 2 (June 1988), pp. 231–247. MR 945111 Zbl 0632.60107 article

: “
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

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

: “
Exponential __\( L_2 \)__ convergence of attractive reversible nearest particle systems,”
Ann. Probab.
17 : 2
(1989),
pp. 403–432.
MR
985371
Zbl
0679.60093
article

Ergodicity of reversible reaction diffusion processes,” Probab. Theory Relat. Fields 85 : 1 (March 1990), pp. 13–26. MR 1044295 Zbl 0669.60077 article

: “
__\( L_2 \)__ 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

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

: “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

: “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

: “The survival of one-dimensional contact processes in random environments,” Ann. Probab. 20 : 2 (1992), pp. 696–723. MR 1159569 Zbl 0754.60126 article

: “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

: “Clustering in one-dimensional threshold voter models,” Stochastic Processes Appl. 42 : 1 (August 1992), pp. 73–90. MR 1172508 Zbl 0752.60086 article

: “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

: “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

: “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

: “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

: “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

: “Charles G. Lange (March 30, 1942–June 25, 1993),” Methods Appl. Anal. 1 : 4 (1994), pp. 387–391. MR 1317018 Zbl 0832.01014 article

: “
The law of large numbers and __\( \sqrt{2} \)__,”
Am. Math. Monthly
102 : 1
(January 1995),
pp. 31–35.
MR
1321453
Zbl
0823.60023
article

Improved upper bounds for the contact process critical value,” Ann. Probab. 23 : 2 (1995), pp. 697–723. MR 1334167 Zbl 0832.60093 article

: “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

: “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

: “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

: “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

: “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

: “Domination by product measures,” Ann. Probab. 25 : 1 (1997), pp. 71–95. MR 1428500 Zbl 0882.60046 article

: “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

: “Ultra logconcave sequences and negative dependence,” J. Combin. Theory Ser. A 79 : 2 (August 1997), pp. 315–325. MR 1462561 Zbl 0888.60013 article

: “
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

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

: “Stochastic interacting systems: Contact, voter and exclusion processes. Grundlehren der Mathematischen Wissenschaften 324. Springer (Berlin), 1999. MR 1717346 Zbl 0949.60006 book

:Monotonicity of conditional distributions and growth models on trees,” Ann. Probab. 28 : 4 (2000), pp. 1645–1665. MR 1813837 Zbl 1044.60094 article

: “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

: “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

: “Characterization of stationary measures for one-dimensional exclusion processes,” Ann. Probab. 30 : 4 (2002), pp. 1539–1575. MR 1944000 Zbl 1039.60086 article

: “Negative correlations and particle systems,” Markov Process. Related Fields 8 : 4 (2002), pp. 547–564. MR 1957219 Zbl 1021.60084 article

: “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

: “Integrals, partitions, and cellular automata,” Trans. Am. Math. Soc. 356 : 8 (2004), pp. 3349–3368. MR 2052953 Zbl 1095.60003 ArXiv math/0302216 article

: “An infinite stochastic model of social network formation,” Stochastic Process. Appl. 113 : 1 (2004), pp. 65–80. MR 2078537 Zbl 1071.60097 article

: “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

: “Interacting particle systems, Reprinted edition. Classics in Mathematics. Springer (New York), 2005. Reprint of the 1985 original. MR 2108619 Zbl 1103.82016 book

: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

: “Exclusion processes in higher dimensions: Stationary measures and convergence,” Ann. Probab. 33 : 6 (2005), pp. 2255–2313. MR 2184097 Zbl 1099.60067 article

: “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

: “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

: “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

: “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

: “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

: “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

: “Distributional limits for the symmetric exclusion process,” Stochastic Process. Appl. 119 : 1 (January 2009), pp. 1–15. MR 2485017 Zbl 1172.60031 article

: “The asymptotic Shapley value for a simple market game,” Econom. Theory 40 : 2 (2009), pp. 333–338. MR 2507870 Zbl 1173.91372 article

: “A stochastic model for phylogenetic trees,” J. Appl. Probab. 46 : 2 (June 2009), pp. 601–607. MR 2535836 Zbl 1180.60079 article

: “Continuous time Markov processes: An introduction. Graduate Studies in Mathematics 113. American Mathematical Society (Providence, RI), 2010. MR 2574430 Zbl 1205.60002 book

: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

: “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

: “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. 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

: “
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

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), \xlink**589** (1977)|MR:0443008, **1464** (1991) and **1608** (1995).
MR
3075635
Zbl
1248.82021
book

The contact process with fast voting,” Electron. J. Probab. 19 (2014), pp. Article no. 28, 19 pages. MR 3174840 Zbl 1291.60203 article

: “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

: “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

: “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

: “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

: “One-dependent colorings of the star graph. Preprint, April 2018. ArXiv 1804.06877 techreport

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

: “