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Here are the slides for my Science Night Live talk.

(probability of having a red coin=60%, probability of going right with red coin=70%, probability of going right with blue coin=40%, periodic boundary conditions)

I'm currently interested in studying random walks in random environments.
Click here for a "popular" presentation of the model.

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Here is my contribution to the field. (a complete list of my publications is here)

• Georgiou N., Rassoul-Agha F., Seppäläinen T. and Yilmaz A. 2013. Ratios of partition functions for the log-gamma polymer. Submitted.
• Rassoul-Agha F. and Seppäläinen T. 2013. Quenched point-to-point free energy for random walks in random potentials. To appear in Probab. Th. Rel. Fields.
• Rassoul-Agha F. and Seppäläinen T. 2012. Quenched point-to-point free energy for random walks in random potentials. (extended version) Preprint.
• Campos D., Drewitz A., Ramírez A.F., Rassoul-Agha F., and Seppäläinen T. 2013. Level 1 quenched large deviation principle for random walk in dynamic random environment. Bull. Inst. Math. Acad. Sin., 8, 1-29. Special Issue in honor of the 70th birthday of Raghu Varadhan.
• Rassoul-Agha F., Seppäläinen T. and Yilmaz A. 2013. Quenched free energy and large deviations for random walks in random potentials. Comm. Pure Appl. Math., 66, 202-244.
• Rassoul-Agha F. and Joseph M. 2011. Almost sure invariance principle for continuous space random walk in dynamic random environment. ALEA Lat. Am. J. Probab. Math. Stat., 8, 43-57.
• Rassoul-Agha F. and Seppäläinen T. 2011. Process-level quenched large deviations for random walk in random environment. Ann. Inst. H. Poincaré Probab. Stat., 47, 214-242.
• Rassoul-Agha F. and Seppäläinen T. 2009. Almost sure functional central limit theorem for ballistic random walk in random environment. Ann. Inst. H. Poincaré Probab. Stat., 45, 373-420.
• Rassoul-Agha F. and Seppäläinen T. 2007. Almost sure functional central limit theorem for non-nestling random walk in random environment. Preprint.
• Rassoul-Agha F. and Seppäläinen T. 2007. Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction. Ann. Probab., 35, 1-31.
• Balázs M., Rassoul-Agha F., and Seppäläinen T. 2006. The random average process and random walk in a space-time random environment in one dimension. Commun. Math. Phys., 266, 499-545.
• Rassoul-Agha F. and Seppäläinen T. 2006. Ballistic random walk in a random environment with a forbidden direction. ALEA Lat. Am. J. Probab. Math. Stat., 1, 111-147.
• Rassoul-Agha F. and Seppäläinen T. 2005. An almost sure invariance principle for random walks in a space-time random environment. Probab. Th. Rel. Fields, 133, 299-314.
• Rassoul-Agha F. 2005. On the zero-one law and the law of large numbers for a random walk in a mixing random environment. Electron. Comm. in Probab., 10, 36-44.
• Rassoul-Agha F. 2004. Large deviations for random walks in a mixing random environment and other (non-Markov) random walks. Comm. Pure Appl. Math., 57, no. 9, 1178-1196.
• Rassoul-Agha F. 2003. The point of view of the particle on the law of large numbers for random walks in a mixing random environment. Ann. Probab., 31, no. 3, 1441-1463.

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Here are more papers on the subject of RWRE. (Click on the journal's name for published version and on the title for the "free" version)

Preprints (in order of appearance)

• Yilmaz A. 2010. Harmonic functions, h-transform and large deviations for random walks in random environments in dimensions four and higher. Ann. Probab. To appear.
• Yilmaz A. 2010. Differing averaged and quenched large deviations for random walks in random environments in dimensions two and three. Commun. Math. Phys., online first.
• Yilmaz A. 2010. Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher. Probab. Th. Rel. Fields, online first.
• Berger N. and Zeitouni O. 2006. A quenched invariance principle for certain ballistic random walks in i.i.d. environments.
• Roitershtein A. 2006. Transient random walks on a strip in a random environment. Ann. Probab. To appear.
• Zeitouni O. 2003. Notes of Rio lectures.

Reprints (in alphabetical order)

• Bandyopadhyay A. and Zeitouni O. 2006. Random Walk in Dynamic Markovian Random Environment. ALEA Lat. Am. J. Probab. Math. Stat., 1, 205-224
• Barlow M. 2004. Random walks on supercritical percolation clusters. Ann. Probab., 32, no. 4, 3024-3084
• Berger N. 2008. Limiting velocity of high dimensional random walk in random environment. Ann. Probab., 36, no. 2, 728-738
• Berger N. and Biskup M. 2007. Quenched invariance principle for simple random walk on percolation clusters. Probab. Th. Rel. Fields, 137, 83-120
• Berger N., Gantert N., and Peres Y. 2003. The speed of biased random walk on percolation clusters. Probab. Th. Rel. Fields, 126, 221-242.
• Biskup M. and Prescott T.M. 2007. CLT for random walk among bounded random conductances. Electron. J. Probab., 12, paper no. 49, 1323-1348.
• Bolthausen E. and Sznitman A-S. 2002. On the static and dynamic points of views for certain random walks in random environment. Methods and Applications of Analysis, 9, no. 3, 345--376
• Bolthausen E., Sznitman A-S., and Zeitouni O. 2003. Cut points and diffusive random walks in random environments. Ann. Inst. H. Poincare Prob. & Stat., 39, 527-555.
• Bolthausen E. and Zeitouni O. 2007. Multiscale analysis of exit distributions for random walks in random environments. Probab. Th. Rel. Fields, 138, 581-645.
• Bramson M., Zeitouni O., and Zerner M.P.W. 2006. Shortest Spanning Trees and a Counterexample for Random Walks in Random Environments. Ann. Probab., 34, no. 3, 821-856
• Comets F., Gantert N. and Zeitouni O. 2000. Quenched, annealed and functional large deviations for one-dimensional random walk in random environment. Probab. Th. Rel. Fields, 118, no. 1, 65-114. (Erratum [ps], 2003)
• Comets F. and Zeitouni O. 2004. A law of large numbers for random walks in random mixing environments. Ann. Probab., 32, 880-914
• Comets F. and Zeitouni O. 2005. Gaussian fluctuations for random walks in random mixing environments. Israel J. Math., 148, 87-114.
• Dembo A., Peres Y. and Zeitouni O. 1996. Tail estimates for one-dimensional random walk in random environment. Commun. Math. Phys. 181, 667-684.
• Gantert N. and Zeitouni O. 1998. Quenched sub-exponential tail estimates for one-dimensional random walk in random environment. Commun. Math. Phys., 194, 177-190.
• Goergen, L. 2006. Limit velocity and zero-one laws for diffusions in random environment. Ann. Appl. Probab., 16, 1086-1123.
• Goergen, L. 2008. An effective criterion and a new example for ballistic diffusions in random environment. Ann. Probab., 36, No. 3, 1093-1133.
• Goldsheid, I. 2007. Simple Transient Random Walks in One-dimensional Random Environment: the Central Limit Theorem. Probab. Th. Rel. Fields, 139, 41-64
• Greven A. and Den Hollander F. 1994. Large deviations for a random walk in random environment. Ann. Probab., 22, No. 3, 1381-1428.
• Joseph M. 2009. Fluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction. Electron. J. Probab., 14, 1268-1281.
• Kalikow S. 1981 Generalized random walk in a random environment. Ann. Probab. 9, No. 5, 753-768.
• Key E. S. 1984. Recurrence and transience criteria for random walk in a random environment. Ann. Probab., 12, No. 2, 529-560.
• Komorowski T. and Krupa G. 2003. The Law of Large Numbers for Ballistic, Multi-dimensional Random Walks on Random Lattices with Correlated Sites. Ann. Inst. H. Poincare Prob. & Stat., 39, 263-285.
• Komorowski T. and Olla S. 2003. A note on the central limit theorem for two-fold stochastic random walks in a random environment. Bull. Polish Acad. Sciences, 51, no. 2.
• Olla S. 2001. Notes on the Central Limit Theorems for Tagged Particles and Diffusions in Random Fields. Given at Etąts de la recherche: Milieux Alčatoires. Panorama et Synthčses, 12, 75-100.
• Peterson J. 2009. Quenched limits for transient, ballistic, sub-gaussian one-dimensional random walk in random environment. Ann. Inst. H. Poincare Prob. & Stat., 45, 685-709.
• Peterson J. and Zeitouni O. 2009. Quenched limits for transient, zero-speed one-dimensional random walk in random environment. Ann. Probab., 37, 143-188.
• Peterson J. and Zeitouni O. 2009. On the annealed large deviation rate function for a multi-dimensional random walk in random environment. ALEA Lat. Am. J. Probab. Math. Stat., 6, 349-368.
• Pisztora A., Povel T. and Zeitouni O. 1999. Precise large deviations estimates for one-dimensional random walk in random environment. Probab. Th. Rel. Fields, 113, 135-170.
• Roitershtein A. 2004. Limit theorems for one-dimensional transient random walks in Markov environments. Ann. Inst. H. Poincare Prob. & Stat., 40, 635-659
• Roitershtein, A. 2005. A log-scale limit theorem for one-dimensional random walks in random environments. Electron. Comm. in Probab., 10, 244-253.
• Schmitz, T. 2006. Diffusions in random environment and ballistic behavior. Ann. Inst. H. Poincare Prob. & Stat., 42, 683-714.
• Schmitz, T. 2006. Examples of condition (T) for diffusions in random environment. Electron. J. Probab., 11, 540-562.
• Shen L. 2002. Asymptotic properties of certain anisotropic walks in random media. Ann. App. Prob., 12, 477-510.
• Sidoravicius V. and Sznitman A-S. 2004. Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Th. Rel. Fields, 129, no. 2, 219-244
• Solomon F. 1975. Random walks in random environment. Ann. Probab., 3, No. 1, 1-31.
• Sznitman A-S. 1998. Brownian motion and random obstacles. Proceedings International Congress of Mathematicians, Berlin 1998, Documenta Mathematica, vol. III, 301-310.
• Sznitman A-S. 1999. Slowdown and neutral pockets for a random walk in random environment. Probab. Th. Rel. Fields, 115, 287-323.
• Sznitman A-S. 2000. Slowdown estimates and central limit theorem for random walks in random environment. J. Eur. Math. Soc., 2, 93-143
• Sznitman A-S. 2001. On a class of transient random walks in random environment. Ann. Probab., 29, no. 2, 724-765.
• Sznitman A-S. 2002. An effective criterion for ballistic behavior of random walks in random environment. Probab. Th. Rel. Fields, 122, no. 4, 509-544.
• Sznitman A-S. 2003. On new examples of ballistic random walks in random environment. Ann. Probab., 31, no. 1, 285-322.
• Sznitman A-S. and Zeitouni O. 2006. An invariance principle for isotropic diffusions in random environments. Invent. Math., 164, 455-567
• Sznitman A-S. and Zerner M.P.W. 1999. A law of large numbers for random walks in random environment. Ann. Probab., 27, 1851-1869.
• Tóth B. 1986. Persistent random walks in random environment. Probab. Th. Rel. Fields, 71, 615-625.
• Varadhan S. R. S. 2003. Large deviations for random walks in a random environment. Comm. Pure Appl. Math., 56, no. 8, 1222-1245.
• Yilmaz A. 2009. Large deviations for random walk in a space-time product environment. Ann. Probab., 37, 189-205.
• Yilmaz A. 2009. Quenched large deviations for random walk in a random environment. Comm. Pure Appl. Math., 62, no. 8, 1033-1075.
• Yilmaz A. 2010. Averaged large deviations for random walk in a random environment. Ann. Inst. H. Poincare Prob. & Stat., 46, 853-868.
• Zerner M.P.W. 1998. Lyapounov exponents and quenched large deviations for multidimensional random walk in random environment. Ann. Appl. Probab., 8, No. 1, 246-280.
• Zerner M.P.W. 1998. Lyapounov exponents and quenched large deviations for multidimensional random walk in random environment. Ann. Probab., 26, No. 4, 1446-1476.
• Zerner M.P.W. 2000. Velocity and Lyapounov exponents of some random walks in random environment. Ann. Inst. H. Poincare Prob. & Stat., 36, No. 6, 737-748.
• Zerner M.P.W. 2002. A non-ballistic law of large numbers for random walks in i.i.d. random environment. Elect. Comm. in Probab., 7, paper no. 19, 191-197
• Zerner M.P.W. 2007. The zero-one law for planar random walks in i.i.d. random environments revisited. Elect. Comm. in Probab., 12, paper no. 32, 326-335
• Zerner M.P.W. and Merkl F. 2001. A zero-one law for planar random walks in random environment. Ann. Probab., 29, No. 4, 1716-1732.

Books and Reviews (in alphabetical order)

• Gantert N. and Zeitouni O. 1999. Large deviations for one-dimentional random walk in a random environment - a survey. Proceedings of the conference on random walks, Budapest, 1998. P. Revesz and B. Toth, editors. Bolyai society mathematical studies 9, 127-165.
• Sznitman A-S. 2006. Topics in random walks in random environment. School and Conference on Probability Theory, 203-266, ICTP Lect. Notes, XVII, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004
• Varadhan S. R. S. 2004. Random walks in a random environment. Proc. Indian Acad. Sci., Math. Sci., 114, No. 4, 309-318.
• Zeitouni O. 2002. Random walks in random environments. Proceedings of the International Congress of Mathematicians, Vol. III 117-127, Higher Ed. Press, Beijing.
• Zeitouni O. 2004. Random walks in random environments (Saint Flour 2001). Lecture Notes in Mathematics, 1837, 189-312, Springer-Verlag, Berlin.
• Zeitouni O. 2006. Random walks in random environments. J. Phys. A, 39, No. 40, R433-R464.

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Last updated June 5, 2008