Some papers and preprints.

Research

1. Multifractal properties of sets of zeroes of Brownian path , (with Vadim Sidorov) Fundamenta Mathematicae 147 (1995) 157-171.
2. Bounded orbits of Anosov flows , Duke Math. J. 87 (1997) 87-114.
3. Entropy of coupled map lattices , J. Stat. Phys. 86 (1997) 377-389.
4. Decay of Correlations
   • On decay of correlations in Anosov flows , Ann. of Math. 147 (1998) 357-390.
   • Prevalence of rapid mixing:
     Part I : Ergodic Theory and Dynamical Systems 18 (1998) 1097-1114.
     Part II : Ergodic Theory and Dynamical Systems 20 (2000) 1045-1059.
   • On mixing properties of compact group extensions of hyperbolic systems , Israel J. Math. , 130 (2002) 157-205.
   • Asymptotic expansion of correlation functions for Z^d covers of hyperbolic flows , (with Peter Nandori and Francoise Pene ) Annales de l'Institut Henri Poincare, Prob. and Stat. 58 (2022) 1244-1283.
   • The central limit theorem and rate of mixing for simple random walks on the circle (with Klaudiusz Czudek), ALEA 21 (2024) 1853-1865.
   • Expanding on average diffeomorphisms on surfaces: exponential mixing (with Jon DeWitt) preprint
5. Mostly contracting diffeomorphisms
   • On dynamics of mostly contracting diffeomorphisms , Comm. in Math. Physics , 213 (2000) 181-201.
   • Geometric and measure-theoretical structures of maps with mostly contracting center , (with Marcelo Viana and Jiagang Yang), Comm. in Math. Physics 341 (2016) 991-1014.
6. Every compact manifold carries a complitely hyperbolic diffeomorphism , (with Yakov Pesin ), Ergodic Theory and Dynamical Systems , 22 (2002) 409-437.
7. Stable accessibility is C1 dense , (with Amie Wilkinson ), Asterisque 287 (2003), 33-60.
8. Limit Theorems for partially hyperbolic systems , Transactions of the AMS 356 (2004) 1637-1689.
9. Perturbation Theory for Invariant measures
   • On differentiability of SRB states for partially hyperbolic systems , Invent. Math. 155 (2004) 389--449.
   • Averaging and Invariant measures , Moscow Math. J. 5 (2005) 537-576.
   • Prelude to a kiss , in Modern dynamical systems (edited by Misha Brin , Boris Hasselblatt and Yakov Pesin ), Cambridge Unversity Press, 2004, 313-324.
   • Anomalous current in periodic Lorentz gases with infinite horizon (with Nikolai Chernov ), Russian Math. Surveys 64 (2009) 651-699.
   • The diffusion coefficient for piecewise expanding maps of the interval with metastable states (with Paul Wright ), Stochastics and Dynamics 12 (2012) paper 1150005.
   • Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps , (with Fabian Contreras), Nonlinearity 29 (2016) 2775-2797.
10. Dynamics of Stochastic Flows (with Vadim Kaloshin and Leonid Koralov)
    • Sample path properties of stochastic flows , Ann. Prob. , 32 (2004) 1-27.
    • Hausdorff Dimension in Stochastic Dispersion , J. Stat. Phys. , 108 (2002) 943-971.
    • A limit shape theorem for periodic stochastic dispersion , CPAM , 57 (2004) 1127-1158.
11. Livsic theory for compact group extensions of hyperbolic systems , Moscow Math. J. 5 (2005) 55-66.
12. On simultaneous linearization of diffeomorphisms of the sphere , (with Raphael Krikorian ), Duke Math. J. , 136 (2007) 475-505.
13. Evolution of adiabatic invariants in stochastic averaging , Stochastics and Dynamics 4 (2004) 265-275.
14. Brownian Brownian Motion-1, (with Nikolai Chernov ), Memoirs AMS, vol. 198, no 927 (2009).
15. Small random perturbations of area preserving flows
    • Avergaging of Hamiltonian flows with an ergodic component , (with Leonid Koralov), Ann. Prob. 36 (2008) 1999-2049.
    • Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus , (with Mark Freidlin and Leonid Koralov), Ergodic Theory and Dynamical Systems , 32 (2012) 899-918.
    • Averaging of incompressible flows on two-dimensional surfaces , (with Leonid Koralov), Journal AMS 26 (2013) 427-449.
16. Dynamics of Lorentz gas
    • Recurrence properties of Lorentz gas (with Domokos Szasz and Tamas Varju), Duke Math. J. 142 (2008) 241-281.
    • Limit Theorems for Locally Perturbed Lorentz processes (with Domokos Szasz and Tamas Varju), Duke Math. J. 148 (2009) 459-499.
    • Non equilibrium density profiles in Lorentz tubes with thermostated boundaries, (with Peter Nandori ) CPAM 69 (2016) 649-692.
17. Fermi acceleration
    • Bouncing balls in non-linear potentials , Discrete and Continuous Dynamical Systems - A 22 (2008) 165-182.
    • Galton board: Limit Theorems and Recurrence , (with Nikolai Chernov ), Journal AMS 22 (2009) 821-858.
    • Motion in a random force field , (with Leonid Koralov ), Nonlinearity 22 (2009) 187-211.
    • Unbounded orbits for semicircular outer billiard , (with ), Annales Henri Poincare 10 (2009) 357-375.
    • Dynamics of some piecewise smooth Fermi-Ulam Models , (with Jacopo de Simoi ), Chaos 22 (2012) paper 026124.
    • Dispersing Fermi-Ulam Models (with Jacopo de Simoi ), to appear in Annales Henri Lebesgue .
18. Particle's drift in self-similar billiards, (with Nikolai Chernov ), Ergodic Theory and Dynamical Systems 28 (2008) 389-403.
19. Repulsion from Resonances , Memoires SMF 128 (2012).
20. Energy transfer in a fast-slow Hamiltonian system (with Carlangelo Liverani ), Comm. Math. Phys. 308 (2011) 201-225.
21. Limit theorems for dispersing billiards with cusps (with Peter Balint and Nikolai Chernov ), Comm. Math. Phys. 308 (2011) 479-510.
22. Random walks in random environment
    • Random walks in Markovian enviroment , (with Carlangelo Liverani ), Elecronic Comm. Prob. 14 (2009) 245-251.
    • Quenched limit theorems for nearest neighbor random walk in 1D random environment, (with Ilya Goldsheid ), Comm. Math. Phys. 315 (2012) 241-277.
    • Limit theorems for random walks on a strip in subdiffusive regime, (with Ilya Goldsheid ), Nonlinearity 26 (2013) 1743-1782.
    • Local limit theorems for random walk in 1D random environment, (with Ilya Goldsheid ), Arxiv der Mathematik 101 (2013) 191-200.
    • Central Limit Theorem for recurrent random walks on a strip with bounded potential, (with Ilya Goldsheid ), Nonlinearity 31 (2018) 3381-3412.
    • Invariant measure for random walks on ergodic environments on a strip, (with Ilya Goldsheid ), Ann. Prob. 47 (2019) 2494-2528.
    • Erratic behavior for 1-dimensional random walks in generic quasi-periodic environment (with Bassam Fayad and Maria Saprykina , Electronic J. Prob. 26 (2021) paper 66, 36pp.
    • Dynamical random walks on integers with a drift (with Davit Karagulyan), Annales de l'Institut Henri Poincare, Prob. and Stat. 59 (2023) 1642--1676.
23. Excited random walks
    • Central Limit Theorem for Excited Random Walk in the Recurrent Regime, ALEA 8 (2011) 259-268.
    • Scaling limits of recurrent excited random walks on integers , (with Elena Kosygina ), Elecronic Comm. Prob. 17 (2012) paper 35.
    • Excursions and occupation times of critical excited random walks , (with Elena Kosygina ), ALEA 12 (2015) 427-450.
24. Convergence of moments for dispersing billiards with cusps , (with Peter Balint and Nikolai Chernov ), Contemporary Mathematics 698 (2017) 35-67.
25. Dynamics of toral translations
    • Deviations of Ergodic sums for ToralTranslations (with Bassam Fayad), part I , GAFA 24 (2014) 85-115, part II , Publications IHES 132 (2020) 293-352.
    • The visits to zero of a random walk driven by an irrational rotation, (with Artur Avila , Eduard Duriev and Omri Sarig ), Israel J. Math. 207 (2015) 653-717.
    • Quenched and annealed temporal limit theorems for circle rotations , (with Omri Sarig ), Asterisque 415 (2020) 57-83.
26. Noncollision singularities in the planar two-center-two-body problem, with Jinxin Xue , Comm. in Math. Physics 345 (2016) 797-879.
27. Asymptotic expansions in Central Limit Theorem
    • A Local Limit Theorem for sum of independent random vectors , Electronic J. Prob. 21 (2016) paper 39.
    • An error term in the Central Limit Theorem for sums of discrete random variables (with Kasun Fernando ) IMRN 21 (2023) 18664--18713.
    • Infinite measure renewal theorem and related results , (with Peter Nandori ), Bulletin LMS 51 (2019) 145-167.
    • On mixing and the local central limit theorem for hyperbolic flows , (with Peter Nandori ), Ergodic Theory and Dynamical Systems 20 (2020) 142-174.
    • Local limit theorems for inhomogeneous Markov chains , (with Omri Sarig ), Springer Lecture Notes in Math. 2331 (2023).
    • Edgeworth expansion for indepenent bounded integer valued random variables (with Yeor Hafouta), SPA 152 (2022) 486-532.
    • A Berry-Esseen theorem and Edgeworth expansions for uniformly elliptic inhomogeneous Markov chains (with Yeor Hafouta), PTRF 186 (2023) 439--476.
    • Berry Esseen theorems for sequences of expanding maps (with Yeor Hafouta), preprint.
    • A local limit theorem for expanding maps (with Yeor Hafouta), preprint.
28. On small gaps in the length spectrum, with Dmitry Jakobson , Journal of Modern Dynamics 10 (2016) 339-352.
29. Central limit theorems for simultaneous Diophantine approximations , (with Bassam Fayad and Ilya Vinogradov ), J. de l'Ecole Polytechnique 4 (2017) 1-35.
30. Temporal Limit Theorems (witt Omri Sarig )
    • Temporal Distributional Limit Theorems for Dynamical Systems J. Stat. Phys. 166 (2017) 680-713.
    • Asymptotic windings of horocycles , Israel J. Math. 228 (2018) 119-176.
31. Multi-type branching processes with time-dependent branching rates (with Pratima Hebbar, Lenid Koralov, and Mark Perlman), J. of Appl. Probability 55 (2018) 701-727.
32. Infinite measure mixing for some mechanical systems (with Peter Nandori ), Adv. Math. . 410 (2022) paper no. 108757.
33. Global observables for random walks: law of large numbers (with Marco Lenci and Peter Nandori ) Annales Institut Henri Poincare Prob. Stat. 57 (2021) 94-115.
34. Multiple Borel Cantelli Lemma in dynamics and multilog law for recurrence (with Bassam Fayad and Sixu Liu), Journal of Modern Dynamics 18 (2022) 209-289.
35. On dynamics of generalized (T, T^{-1}) transformations of generalized (T, T^{-1}) transformations
    • Mixing properties (with Changguang Dong, Adam Kanigowski and Peter Nandori ) Israel J. Math. 247 (2022) 21-73.
    • Flexibility of statistical properties for smooth systems satisfying the central limit theorem (with Changguang Dong, Adam Kanigowski and Peter Nandori ), Inv. Math. 230 (2022) 31-120.
    • Smooth zero entropy flows satisfying the classical central limit theorem (with Bassam Fayad and Adam Kanigowski), to appear in Journal de l'Ecole Polytechnique .
    • Limit Theorems for low dimensional generalized $T,T^{-1}$ transformations (with Changguang Dong, Adam Kanigowski and Peter Nandori ), preprint.
36. Exponential mixing implies Bernoulli with Adam Kanigowski and Federico Rodriguez Hertz, to appear in Ann. Math.

Expositiory

1. Addendum to the paper Periodic points and dynamical spectra , by Viviane Baladi (with Mark Pollicott ) Ergodic Theory and Dynamical Systems 18 (1998) 293-301.
2. Addendum to the paper Lectures on Lyapunov exponents and smooth ergodic theory by Luis Barreira and Yakov Pesin (with Hyui Hu and Yakov Pesin ), Proceedings of Symposia in Pure Mathematics 69 (2001) 95-106.
3. Lectures on u-Gibbs states , Evanston, May 31-June 2, 2001.
4. Sample path properties of random transformations , Kyoto, August 12, 2002,
5. Introduction to averaging , Institut Henri Poincare, april-july 2005.
6. Stable ergodicity for partially hyperbolic attractors with negative central exponents , (with Keith Burns , Yakov Pesin and Mark Pollicott ), J. Modern Dynamics 2 (2008) 63-81.
7. Hyperbolic billiards and statistical physics , (with Nikolai Chernov ), ICM, Madrid, August 2006.
8. Diffusive motion and recurrence on generalized Galton board , (with Nikolai Chernov ), Phys. Rev. Lett. , 99 (2007) paper 030601.
9. Fermi acceleration , Canadian Mathematical Society Winter Meeting. December 2006.
10. Limit Theorems for Hyperbolic Systems, Beijing, August 2009.
11. Piecewise smooth perturbations of integrable systems, International Congress of Mathematical Physics, Aalborg, Denmark, August 2012.
12. Lectures on Bouncing Balls, Murcia, Spain, January 2013.
13. Limit theorems for toral translations (with Bassam Fayad), Lousagne, June 2013.
14. Notes on Bjorklund-Gorodnik Central Limit Thereom .