Research Output per year

## Research Output

## Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium

Bakhtin, Y. & Gaál, A., Jan 1 2019, (Accepted/In press) In : Stochastics and Dynamics. 2050026.Research output: Contribution to journal › Article

## Malliavin calculus approach to long exit times from an unstable equilibrium

Bakhtin, Y. & Pajor-Gyulai, Z., Apr 1 2019, In : Annals of Applied Probability. 29, 2, p. 827-850 24 p.Research output: Contribution to journal › Article

## Thermodynamic Limit for Directed Polymers and Stationary Solutions of the Burgers Equation

Bakhtin, Y. & Li, L., Mar 2019, In : Communications on Pure and Applied Mathematics. 72, 3, p. 536-619 84 p.Research output: Contribution to journal › Article

## Transversal fluctuations for a first passage percolation model

Bakhtin, Y. & Wu, W., May 1 2019, In : Annales de l'institut Henri Poincare (B) Probability and Statistics. 55, 2, p. 1042-1060 19 p.Research output: Contribution to journal › Review article

## Universal Statistics of Incubation Periods and Other Detection Times via Diffusion Models

Bakhtin, Y., Apr 15 2019, In : Bulletin of Mathematical Biology. 81, 4, p. 1070-1088 19 p.Research output: Contribution to journal › Article

## Ergodicity and Hopf–Lax–Oleinik formula for fluid flows evolving around a black hole under a random forcing

Bakhtin, Y. & LeFloch, P. G., Dec 1 2018, In : Stochastics and Partial Differential Equations: Analysis and Computations. 6, 4, p. 746-785 40 p.Research output: Contribution to journal › Article

## On global solutions of the random Hamilton-Jacobi equations and the KPZ problem

Bakhtin, Y. & Khanin, K., Feb 19 2018, In : Nonlinearity. 31, 4, p. R93-R121Research output: Contribution to journal › Article

## Scaling limit for escapes from unstable equilibria in the vanishing noise limit: Nontrivial Jordan block case

Bakhtin, Y. & Pajor-Gyulai, Z., Jan 1 2018, (Accepted/In press) In : Stochastics and Dynamics.Research output: Contribution to journal › Article

## Smooth invariant densities for random switching on the torus

Bakhtin, Y., Hurth, T., Lawley, S. D. & Mattingly, J. C., Feb 20 2018, In : Nonlinearity. 31, 4, p. 1331-1350 20 p.Research output: Contribution to journal › Article

## Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers Equation

Bakhtin, Y. & Li, L., Sep 1 2018, In : Journal of Statistical Physics. 172, 5, p. 1358-1397 40 p.Research output: Contribution to journal › Article

## Inviscid burgers equation with random kick forcing in Noncompact setting

Bakhtin, Y., 2016, In : Electronic Journal of Probability. 21, 37.Research output: Contribution to journal › Article

## Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations

Bakhtin, Y. & Święch, A., 2016, In : Transactions of the American Mathematical Society. 368, 9, p. 6487-6517 31 p.Research output: Contribution to journal › Article

## Ergodic theory of the Burgers equation

Bakhtin, Y., 2015, (Accepted/In press)*Lecture notes for summer school on probability and statistical physics in St. Petersburg, 2012.*Sidoravicius, V. & Smirnov, S. (eds.). Forthcoming

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)

## Regularity of invariant densities for 1D systems with random switching

Bakhtin, Y., Hurth, T. & Mattingly, J. C., Sep 30 2015, In : Nonlinearity. 28, 11, p. 3755-3787 33 p.Research output: Contribution to journal › Article

## Inviscid Burgers equation with random kick forcing in noncompact setting

Bakhtin, Y., Jun 22 2014, In : arXiv. 1406.5660.Research output: Contribution to journal › Article

## Chapter 12: Geometry of large random trees: SPDE approximation

Bakhtin, Y., 2013,*Stochastic Geometry, Spatial Statistics and Random Fields: Asymptotic Methods.*Springer Verlag, p. 399-440 42 p. (Lecture Notes in Mathematics; vol. 2068).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

## Geometry of Large Random Trees: SPDE Approximation

Bakhtin, Y., Jan 1 2013,*Stochastic Geometry, Spatial Statistics and Random Fields: Asymptotic Methods.*Springer-Verlag, p. 399-420 22 p. (Lecture Notes in Mathematics; vol. 2068).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

## Gumbel distribution in exit problems

Bakhtin, Y., Jul 26 2013, In : arXiv. 1307.7060.Research output: Contribution to journal › Article

## Scaling limits for conditional diffusion exit problems, Doob's h-transform, and asymptotics for nonlinear elliptic equations

Bakhtin, Y. & Swiech, A., Oct 22 2013, In : arXiv. 1310.6023.Research output: Contribution to journal › Article

## Space-time stationary solutions for the Burgers equation

Bakhtin, Y., Cator, E. & Khanin, K., Oct 15 2013, In : Journal of the American Mathematical Society. 27, 1, p. 193-238 46 p.Research output: Contribution to journal › Article

## The burgers equation with poisson random forcing

Bakhtin, Y., Aug 20 2013, In : Annals of Probability. 41, 4, p. 2961-2989 29 p.Research output: Contribution to journal › Article

## A neural computation model for decision-making times

Bakhtin, Y. & Correll, J., Oct 1 2012, In : Journal of Mathematical Psychology. 56, 5, p. 333-340 8 p.Research output: Contribution to journal › Article

## Decision Making Times in Mean-Field Dynamic Ising Model

Bakhtin, Y., Jul 1 2012, In : Annales Henri Poincare. 13, 5, p. 1291-1303 13 p.Research output: Contribution to journal › Article

## Invariant densities for dynamical systems with random switching

Bakhtin, Y. & Hurth, T., Oct 1 2012, In : Nonlinearity. 25, 10, p. 2937-2952 16 p.Research output: Contribution to journal › Article

## Noisy heteroclinic networks

Bakhtin, Y., Jun 1 2011, In : Probability Theory and Related Fields. 150, 1-2, p. 1-42 42 p.Research output: Contribution to journal › Article

## Normal forms approach to diffusion near hyperbolic equilibria

Monter, S. A. A. & Bakhtin, Y., Jun 1 2011, In : Nonlinearity. 24, 6, p. 1883-1907 25 p.Research output: Contribution to journal › Article

## Scaling limit for the diffusion exit problem in the Levinson case

Monter, S. A. A. & Bakhtin, Y., Jan 1 2011, In : Stochastic Processes and their Applications. 121, 1, p. 24-37 14 p.Research output: Contribution to journal › Article

## SPDE approximation for random trees

Bakhtin, Y., 2011, In : Markov Processes and Related Fields. 17, 1, p. 1-36Research output: Contribution to journal › Article

## The Optimal Sink and the Best Source in a Markov Chain

Bakhtin, Y. & Bunimovich, L., Jun 1 2011, In : Journal of Statistical Physics. 143, 5, p. 943-954 12 p.Research output: Contribution to journal › Article

## Localization and perron-frobenius theory for directed polymers

Bakhtin, Y. & Khanin, K., Dec 1 2010, In : Moscow Mathematical Journal. 10, 4, p. 667-686 20 p.Research output: Contribution to journal › Article

## Poisson limit for associated random fields

Bakhtin, Y., Dec 1 2010, In : Theory of Probability and its Applications. 54, 4, p. 678-681 4 p.Research output: Contribution to journal › Article

## Small noise limit for diffusions near heteroclinic networks

Bakhtin, Y., Sep 1 2010, In : Dynamical Systems. 25, 3, p. 413-431 19 p.Research output: Contribution to journal › Article

## Solutions of semilinear wave equation via stochastic cascades

Bakhtin, Y. & Mueller, C., 2010, In : Communications on Stochastic Analysis. 4, 3, p. 425-431Research output: Contribution to journal › Article

## Thermodynamic limit for large random trees

Bakhtin, Y., Oct 1 2010, In : Random Structures and Algorithms. 37, 3, p. 312-331 20 p.Research output: Contribution to journal › Article

## Large deviations for random trees and the branching of RNA secondary structures

Bakhtin, Y. & Heitsch, C. E., Jan 1 2009, In : Bulletin of Mathematical Biology. 71, 1, p. 84-106 23 p.Research output: Contribution to journal › Article

## A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Bakhtin, Y. & Martínez, M., Dec 1 2008, In : Annales de l'institut Henri Poincare (B) Probability and Statistics. 44, 6, p. 1078-1089 12 p.Research output: Contribution to journal › Article

## Exit asymptotics for small diffusion about an unstable equilibrium

Bakhtin, Y., May 1 2008, In : Stochastic Processes and their Applications. 118, 5, p. 839-851 13 p.Research output: Contribution to journal › Article

## Large deviations for random trees

Bakhtin, Y. & Heitsch, C., Aug 1 2008, In : Journal of Statistical Physics. 132, 3, p. 551-560 10 p.Research output: Contribution to journal › Article

## Self-similar Markov processes on Cantor set

Bakhtin, Y., Oct 17 2008, In : arXiv. 0810.3260.Research output: Contribution to journal › Article

## Burgers equation with random boundary conditions

Bakhtin, Y., Jul 1 2007, In : Proceedings of the American Mathematical Society. 135, 7, p. 2257-2262 6 p.Research output: Contribution to journal › Article

## Malliavin calculus for infinite-dimensional systems with additive noise

Bakhtin, Y. & Mattingly, J. C., Aug 15 2007, In : Journal of Functional Analysis. 249, 2, p. 307-353 47 p.Research output: Contribution to journal › Article

## Existence and uniqueness of stationary solutions for 3D Navier-Stokes system with small random Forcing via stochastic cascades

Bakhtin, Y., Jan 1 2006, In : Journal of Statistical Physics. 122, 2, p. 351-360 10 p.Research output: Contribution to journal › Article

## Lyapunov exponents for stochastic differential equations with infinite memory and application to stochastic Navier-stokes equations

Bakhtin, Y., Jul 2006, In : Discrete and Continuous Dynamical Systems - Series B. 6, 4, p. 697-709 13 p.Research output: Contribution to journal › Article

## Regularity of solutions to vorticity navier-stokes system on ℝ^{2}

Arnold, M., Bakhtin, Y. & Dinaburg, E., Sep 1 2005, In : Communications In Mathematical Physics. 258, 2, p. 339-348 10 p.Research output: Contribution to journal › Article

## Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations

Bakhtin, Y. & Mattingly, J. C., Oct 1 2005, In : Communications in Contemporary Mathematics. 7, 5, p. 553-582 30 p.Research output: Contribution to journal › Article

## On solutions with infinite energy and enstrophy of the Navier-Stokes system

Bakhtin, Y. Y., Dinaburg, E. I. & Sinai, Y. G., Nov 1 2004, In : Russian Mathematical Surveys. 59, 6, p. 1061-1078 18 p.Research output: Contribution to journal › Article

## Regularity of solutions of the Navier-Stokes system on the plane

Arnol'd, M. D., Bakhtin, Y. Y. & Dinaburg, E. I., May 1 2004, In : Russian Mathematical Surveys. 59, 3, p. 560-561 2 p.Research output: Contribution to journal › Article

## Existence and uniqueness of a stationary solution of a nonlinear stochastic differential equation with memory

Bakhtin, Y., Jan 1 2003, In : Theory of Probability and its Applications. 47, 4, p. 684-688 5 p.Research output: Contribution to journal › Article

## A functional central limit theorem for transformed solutions of the multidimensional Burgers equation with random initial data

Bakhtin, Y. Y., Jan 1 2002, In : Theory of Probability and its Applications. 46, 3, p. 387-405 19 p.Research output: Contribution to journal › Article

## A functional central limit theorem for parabolically rescaled random solutions of the Burgers equation

Bakhtin, Y., 2001,*Abstracts of XXI Seminar on Stability Problems of Stochastic Models, Eger, 2001.*p. 30-31

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution