Celebratio Mathematica

S. R. Srinivasa Varadhan

Probability and statistics

Large deviations

Filter the Bibliography List

clear

S. R. S. Varadhan: “Dif­fu­sion pro­cesses in a small time in­ter­val,” Comm. Pure Ap­pl. Math. 20 : 4 (November 1967), pp. 659–​685. MR 0217881 Zbl 0278.​60051 article

S. R. S. Varadhan: “On the be­ha­vi­or of the fun­da­ment­al solu­tion of the heat equa­tion with vari­able coef­fi­cients,” Comm. Pure Ap­pl. Math. 20 : 2 (May 1967), pp. 431–​455. MR 0208191 Zbl 0155.​16503 article

M. D. Don­sker and S. R. S. Varadhan: “Asymp­tot­ic eval­u­ation of cer­tain Markov pro­cess ex­pect­a­tions for large time. I,” Comm. Pure Ap­pl. Math. 28 : 1 (January 1975), pp. 1–​47. MR 0386024 article

M. D. Don­sker and S. R. S. Varadhan: “Er­rat­um: ‘Asymp­tot­ics for the Wien­er saus­age’,” Comm. Pure Ap­pl. Math. 28 : 5 (September 1975), pp. 677. MR 0397902 article

M. D. Don­sker and S. R. S. Varadhan: “Asymp­tot­ics for the Wien­er saus­age,” Comm. Pure Ap­pl. Math. 28 : 4 (July 1975), pp. 525–​565. MR 0397901 article

M. D. Don­sker and S. R. S. Varadhan: “Large de­vi­ations for Markov pro­cesses and the asymp­tot­ic eval­u­ation of cer­tain Markov pro­cess ex­pect­a­tions for large times,” pp. 82–​88 in Prob­ab­il­ist­ic meth­ods in dif­fer­en­tial equa­tions (Vic­tor­ia, BC, Au­gust 19–20, 1974). Edi­ted by M. A. Pin­sky. Lec­ture Notes in Math­em­at­ics 451. Spring­er (Ber­lin), 1975. MR 0410942 incollection

M. D. Don­sker and S. R. S. Varadhan: “On a vari­ation­al for­mula for the prin­cip­al ei­gen­value for op­er­at­ors with max­im­um prin­ciple,” Proc. Nat. Acad. Sci. U.S.A. 72 (1975), pp. 780–​783. MR 0361998 Zbl 0353.​49039 article

M. D. Don­sker and S. R. S. Varadhan: “On some prob­lems of large de­vi­ations for Markov pro­cesses,” pp. 409–​416, 417–​418 in Pro­ceed­ings of the 40th ses­sion of the In­ter­na­tion­al Stat­ist­ic­al In­sti­tute (Warsaw, 1975), published as Bul­let­in of the In­ter­na­tion­al Stat­ist­ic­al In­sti­tute 46 : 1. Hérit­i­ers Botta, 1975. MR 0488298 Zbl 0351.​60036 inproceedings

M. D. Don­sker and S. R. S. Varadhan: “Asymp­tot­ic eval­u­ation of cer­tain Wien­er in­teg­rals for large time,” pp. 15–​33 in Func­tion­al in­teg­ra­tion and its ap­plic­a­tions (Lon­don, April 1974). Edi­ted by A. M. Ar­thurs. Clar­en­don Press (Ox­ford), 1975. MR 0486395 Zbl 0333.​60078 incollection

M. D. Don­sker and S. R. S. Varadhan: “Asymp­tot­ic eval­u­ation of cer­tain Markov pro­cess ex­pect­a­tions for large time. III,” Comm. Pure Ap­pl. Math. 29 : 4 (July 1976), pp. 389–​461. MR 0428471 Zbl 0348.​60032 article

M. D. Don­sker and S. R. S. Varadhan: “On the prin­cip­al ei­gen­value of second-or­der el­lipt­ic dif­fer­en­tial op­er­at­ors,” Comm. Pure Ap­pl. Math. 29 : 6 (November 1976), pp. 595–​621. MR 0425380 Zbl 0356.​35065 article

M. D. Don­sker and S. R. S. Varadhan: “Some prob­lems of large de­vi­ations,” pp. 313–​318 (IN­DAM, Rome, 1975). Sym­po­sia Math­em­at­ica 21. Aca­dem­ic Press (Lon­don), 1977. MR 0517541 Zbl 0372.​60036 incollection

G. C. Papan­ic­ol­aou, D. Stroock, and S. R. S. Varadhan: “Mar­tin­gale ap­proach to some lim­it the­or­ems,” pp. ii+120 pp. in Duke tur­bu­lence con­fer­ence (Durham, NC, April 23–25, 1976). Edi­ted by P. L. Chow. Duke Uni­versity Math­em­at­ics Series III. Duke Uni­versity (Durham, NC), 1977. MR 0461684 incollection

M. D. Don­sker and S. R. S. Varadhan: “On laws of the it­er­ated log­ar­ithm for loc­al times,” Comm. Pure Ap­pl. Math. 30 : 6 (November 1977), pp. 707–​753. MR 0461682 Zbl 0356.​60029 article

M. D. Don­sker and S. R. S. Varadhan: “On the prin­cip­al ei­gen­value of el­lipt­ic second or­der dif­fer­en­tial op­er­at­ors,” pp. 41–​47 in Pro­ceed­ings of the in­ter­na­tion­al sym­posi­um on stochast­ic dif­fer­en­tial equa­tions (Kyoto, 1976). Edi­ted by K. Itō. Wiley (New York), 1978. MR 536002 Zbl 0447.​35030 inproceedings

J. Saint-Ray­mond: “Quelques re­marques sur un art­icle de M. D. Don­sker et S. R. S. Varadhan: ‘Asymp­tot­ic eval­u­ation of cer­tain Markov pro­cess ex­pect­a­tions for large time, III’,” pp. 468–​481 in Sémin­aire de prob­ab­il­ités, XII (Stras­bourg, 1976/1977). Edi­ted by C. Del­lacher­ie, P. A. Mey­er, and M. Weil. Lec­ture Notes in Math­em­at­ics 649. Spring­er (Ber­lin), 1978. MR 520021 incollection

M. D. Don­sker and S. R. S. Varadhan: “On the num­ber of dis­tinct sites vis­ited by a ran­dom walk,” Comm. Pure Ap­pl. Math. 32 : 6 (1979), pp. 721–​747. MR 539157 Zbl 0418.​60074 article

M. D. Don­sker and S. R. S. Varadhan: “A law of the it­er­ated log­ar­ithm for total oc­cu­pa­tion times of tran­si­ent Browni­an mo­tion,” Comm. Pure Ap­pl. Math. 33 : 3 (1980), pp. 365–​393. MR 562740 Zbl 0504.​60037 article

S. R. S. Varadhan: “Some prob­lems of large de­vi­ations,” pp. 755–​762 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Hel­sinki, 1978), vol. 2. Edi­ted by O. Le­hto. Acad. Sci. Fen­nica (Hel­sinki), 1980. MR 562683 Zbl 0421.​60025 inproceedings

M. D. Don­sker and S. R. S. Varadhan: “The po­laron prob­lem and large de­vi­ations,” Phys. Rep. 77 : 3 (November 1981), pp. 235–​237. MR 639028 article

M. D. Don­sker and S. R. S. Varadhan: “Some prob­lems of large de­vi­ations,” pp. 41–​46 in Stochast­ic dif­fer­en­tial sys­tems (Visegrád, Hun­gary, Septem­ber 15–20, 1980). Edi­ted by M. Ar­ató, D. Ver­mes, and A. V. Bal­akrish­nan. Lec­ture Notes in Con­trol and In­form­a­tion Sci­ences 36. Spring­er (Ber­lin), 1981. MR 653644 Zbl 0472.​60028 incollection

S. R. S. Varadhan: “Large de­vi­ations,” pp. 382–​392 in Ad­vances in fil­ter­ing and op­tim­al stochast­ic con­trol (Cocoyoc, Mex­ico, Feb­ru­ary 1–6, 1982). Edi­ted by W. H. Flem­ing and L. G. Goros­tiza. Lec­ture Notes in Con­trol and In­form­a­tion Sci­ences 42. Spring­er (Ber­lin), 1982. MR 794532 Zbl 0496.​60024 incollection

M. D. Don­sker and S. R. S. Varadhan: “Asymp­tot­ics for the po­laron,” Comm. Pure Ap­pl. Math. 36 : 4 (1983), pp. 505–​528. MR 709647 Zbl 0538.​60081 article

S. R. S. Varadhan: Large de­vi­ations and ap­plic­a­tions. CBMS-NSF Re­gion­al Con­fer­ence Series in Ap­plied Math­em­at­ics 46. So­ci­ety for In­dus­tri­al and Ap­plied Math­em­at­ics (Phil­adelphia, PA), 1984. MR 758258 Zbl 0549.​60023 book

S. R. S. Varadhan: “Large de­vi­ations and ap­plic­a­tions,” Ex­pos­i­tion. Math. 3 : 3 (1985), pp. 251–​272. MR 861018 Zbl 0567.​60030 article

M. D. Don­sker and S. R. S. Varadhan: “Large de­vi­ations for sta­tion­ary Gaus­si­an pro­cesses,” pp. 108–​112 in Stochast­ic dif­fer­en­tial sys­tems (Mar­seille-Lu­miny, 1984). Edi­ted by M. Mét­ivi­er and É. Par­doux. Lec­ture Notes in Con­trol and In­form­a­tion Sci­ences 69. Spring­er (Ber­lin), 1985. MR 798313 Zbl 0657.​60036 incollection

S. R. S. Varadhan: “Stochast­ic dif­fer­en­tial equa­tions–large de­vi­ations,” pp. 625–​678 in Phénomènes cri­tiques, sys­tèmes aléatoires, théor­ies de jauge (Les Houches, 1984), Part II. Edi­ted by K. Os­ter­walder, R. Stora, and D. Bry­dges. North-Hol­land (Am­s­ter­dam), 1986. MR 880536 incollection

M. D. Don­sker and S. R. S. Varadhan: “Large de­vi­ations for non­in­ter­act­ing in­fin­ite-particle sys­tems,” J. Stat­ist. Phys. 46 : 5–​6 (1987), pp. 1195–​1232. MR 893138 Zbl 0682.​60020 article

S. R. S. Varadhan: “Large de­vi­ations and ap­plic­a­tions,” pp. 1–​49 in École d’été de prob­ab­il­ités de Saint-Flour XV–XVII, 1985–87 (Saint-Flour, France, 1985–87). Edi­ted by P.-L. Hen­nequin. Lec­ture Notes in Math­em­at­ics 1362. Spring­er (Ber­lin), 1988. MR 983371 Zbl 0661.​60040 incollection

C. Kipnis, S. Olla, and S. R. S. Varadhan: “Hy­dro­dynam­ics and large de­vi­ation for simple ex­clu­sion pro­cesses,” Comm. Pure Ap­pl. Math. 42 : 2 (1989), pp. 115–​137. MR 978701 Zbl 0644.​76001 article

M. D. Don­sker and S. R. S. Varadhan: “Large de­vi­ations from a hy­dro­dynam­ic scal­ing lim­it,” Comm. Pure Ap­pl. Math. 42 : 3 (April 1989), pp. 243–​270. MR 982350 Zbl 0780.​60027 article

J. R. Bax­ter, N. C. Jain, and S. R. S. Varadhan: “Some fa­mil­i­ar ex­amples for which the large de­vi­ation prin­ciple does not hold,” Comm. Pure Ap­pl. Math. 44 : 8–​9 (1991), pp. 911–​923. MR 1127039 Zbl 0749.​60025 article

J. Quastel, F. Reza­khan­lou, and S. R. S. Varadhan: “Large de­vi­ations for the sym­met­ric simple ex­clu­sion pro­cess in di­men­sions \( d\geq 3 \),” Probab. The­ory Re­lated Fields 113 : 1 (1999), pp. 1–​84. MR 1670733 Zbl 0928.​60087 article

S. R. S. Varadhan: “Large de­vi­ations for in­ter­act­ing particle sys­tems,” pp. 373–​383 in Per­plex­ing prob­lems in prob­ab­il­ity. Edi­ted by M. Bramson and R. Dur­rett. Pro­gress in Prob­ab­il­ity 44. Birkhäuser (Bo­ston, MA), 1999. MR 1703141 Zbl 0941.​60096 incollection

S. R. S. Varadhan: “Large de­vi­ation and hy­dro­dynam­ic scal­ing,” pp. 265–​286 in Tanigu­chi con­fer­ence on math­em­at­ics Nara ’98 (Nara, Ja­pan, Decem­ber 15–20, 1998). Edi­ted by M. Maruyama and T. Sunada. Ad­vanced Stud­ies in Pure Math­em­at­ics 31. Math­em­at­ic­al So­ci­ety of Ja­pan (Tokyo), 2001. MR 1865096 Zbl 1006.​60019 incollection

S. R. S. Varadhan: “Rare events, large de­vi­ations,” pp. 85–​92 in Math­em­at­ic­al fin­ance — Bacheli­er Con­gress 2000 (Par­is, June 29–Ju­ly 1, 2000). Edi­ted by H. Ge­man, D. Madan, S. R. Pliska, and T. Vorst. Spring­er Fin­ance. Spring­er (Ber­lin), 2002. MR 1960560 incollection

S. R. S. Varadhan: “Large de­vi­ations and en­tropy,” pp. 199–​214 in En­tropy. Edi­ted by A. Gre­ven, G. Keller, and G. War­necke. Prin­ceton Series in Ap­plied Math­em­at­ics. Prin­ceton Uni­versity Press, 2003. MR 2035822 Zbl 1163.​60312 incollection

S. R. S. Varadhan: “Large de­vi­ations for ran­dom walks in a ran­dom en­vir­on­ment,” Comm. Pure Ap­pl. Math. 56 : 8 (August 2003), pp. 1222–​1245. Ded­ic­ated to the memory of Jür­gen K. Moser. MR 1989232 Zbl 1042.​60071 article

S. R. S. Varadhan: “Large de­vi­ations for the asym­met­ric simple ex­clu­sion pro­cess,” pp. 1–​27 in Stochast­ic ana­lys­is on large scale in­ter­act­ing sys­tems. Edi­ted by T. Fun­aki and H. Os­ada. Ad­vanced Stud­ies in Pure Math­em­at­ics 39. Math. Soc. Ja­pan (Tokyo), 2004. MR 2073328 Zbl 1114.​60026 incollection

E. Kosy­gina, F. Reza­khan­lou, and S. R. S. Varadhan: “Stochast­ic ho­mo­gen­iz­a­tion of Hamilton–Jac­obi–Bell­man equa­tions,” Comm. Pure Ap­pl. Math. 59 : 10 (2006), pp. 1489–​1521. MR 2248897 Zbl 1111.​60055 article

S. R. S. Varadhan: “Large de­vi­ations,” Ann. Probab. 36 : 2 (2008), pp. 397–​419. MR 2393987 Zbl 1146.​60003 ArXiv 0804.​2330 article

E. Kosy­gina and S. R. S. Varadhan: “Ho­mo­gen­iz­a­tion of Hamilton–Jac­obi–Bell­man equa­tions with re­spect to time-space shifts in a sta­tion­ary er­god­ic me­di­um,” Comm. Pure Ap­pl. Math. 61 : 6 (2008), pp. 816–​847. MR 2400607 Zbl 1144.​35008 article

S. R. S. Varadhan: “Large de­vi­ations and scal­ing lim­it,” Lett. Math. Phys. 88 : 1–​3 (2009), pp. 175–​185. MR 2512145 Zbl 1185.​60024 article

S. R. S. Varadhan: “Work­shop on large de­vi­ations: Lec­ture notes,” pp. 1–​14 in Pro­ceed­ings of the in­ter­na­tion­al sym­posi­um on prob­ab­il­ity the­ory and stochast­ic pro­cesses (Coch­in Uni­versity of Sci­ence and Tech­no­logy, Ko­chi, In­dia, Feb­ru­ary 6–9, 2009), published as Bull. Ker­ala Math. As­soc. Special Issue. Issue edi­ted by S. R. S. Varadhan. 2009. MR 2590249 incollection

Y. Kifer and S. R. S. Varadhan: Non­con­ven­tion­al lim­it the­or­ems in dis­crete and con­tinu­ous time via mar­tin­gales. Pre­print, December 2010. ArXiv 1012.​2223 techreport

S. R. S. Varadhan: “Large de­vi­ations,” pp. 622–​639 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Hy­dera­bad, In­dia, Au­gust 19–27, 2010), vol. I: Plen­ary lec­tures and ce­re­mon­ies. Edi­ted by R. Bha­tia. Hindus­tan Book Agency (New Del­hi), 2010. MR 2827907 Zbl 1228.​60037 inproceedings

D. Stroock and S. R. S. Varadhan: “The­ory of dif­fu­sion pro­cesses,” pp. 149–​191 in Stochast­ic dif­fer­en­tial equa­tions (Cor­tona, Italy, May 29–June 10, 1978). Edi­ted by J. Cec­coni. CI­ME Sum­mer Schools 77. Spring­er (Heidel­berg), 2010. MR 2830392 incollection

S. Chat­ter­jee and S. R. S. Varadhan: Large de­vi­ations for ran­dom matrices. Pre­print, June 2011. ArXiv 1106.​4366 techreport

S. Se­th­ura­man and S. R. S. Varadhan: Large de­vi­ations for the cur­rent and tagged particle in 1D nearest-neigh­bor sym­met­ric simple ex­clu­sion. Pre­print, January 2011. ArXiv 1101.​1479 techreport