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Yuri Bakhtin

Associate Professor of Mathematics

    19972019
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    Research Output 1997 2019

    2019

    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

    Exit Time
    Dynamical systems
    Dynamical system
    Unstable
    Exit Problem

    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

    Exit Time
    Malliavin Calculus
    Tail
    Vector Field
    Unstable

    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

    First-passage Percolation
    Exponent
    Fluctuations
    Model
    Estimate
    2018

    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

    Ergodicity
    Forcing
    Black Holes
    Fluid Flow
    Flow of fluids

    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-R121

    Research output: Contribution to journal › Article

    Hamilton-Jacobi equation
    Hamilton-Jacobi Equation
    Global Solution
    Directed Polymers
    Hamiltonians

    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

    Jordan Block
    Nonlinear dynamical systems
    Scaling Limit
    White noise
    Linearization

    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

    Torus
    Invariant
    Vector Field
    Integration by Parts Formula
    poisson process

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

    Bakhtin, Y. & Li, L., Jan 1 2018, (Accepted/In press) In : Communications on Pure and Applied Mathematics.

    Research output: Contribution to journal › Article

    Directed Polymers
    Polymer Solution
    Thermodynamic Limit
    Burgers Equation
    Stationary Solutions

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

    Bakhtin, Y., Jan 1 2018, (Accepted/In press) In : Bulletin of Mathematical Biology.

    Research output: Contribution to journal › Article

    Diffusion Model
    Exit Time
    statistics
    incubation
    Statistics

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

    Bakhtin, Y. & Li, L., Jul 5 2018, (Accepted/In press) In : Journal of Statistical Physics. p. 1-40 40 p.

    Research output: Contribution to journal › Article

    Inviscid Limit
    Directed Polymers
    Burger equation
    Burgers Equation
    Stationary Solutions
    2016

    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

    Burgers Equation
    Minimizer
    Forcing
    Hyperbolicity
    Ergodic Theory

    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

    H-transform
    Exit Problem
    Nonlinear Elliptic Equations
    Scaling Limit
    Diffusion Problem
    2015

    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

    regularity
    Critical point
    critical point
    Dynamical systems
    Regularity
    2014

    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

    Burgers Equation
    Minimizer
    Forcing
    Hyperbolicity
    Ergodic Theory
    2013

    Chapter 12: Geometry of large random trees: SPDE approximation

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

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

    Random Trees
    Approximation
    Brownian Sheet
    Stochastic PDEs
    Superprocess

    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

    Random Trees
    Approximation
    Brownian Sheet
    Stochastic PDEs
    Superprocess

    Gumbel distribution in exit problems

    Bakhtin, Y., Jul 26 2013, In : arXiv. 1307.7060.

    Research output: Contribution to journal › Article

    Exit Problem
    Gumbel Distribution
    Exit Time
    Extreme Values

    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

    H-transform
    Exit Problem
    Nonlinear Elliptic Equations
    Scaling Limit
    Diffusion Problem

    Space-time stationary solutions for the Burgers equation

    Bakhtin, Y., Cator, E. & Khanin, K., 2013, In : Journal of the American Mathematical Society. 27, 1, p. 193-238 46 p.

    Research output: Contribution to journal › Article

    Burgers Equation
    Stationary Solutions
    Global Solution
    Markov processes
    Space-time

    The burgers equation with poisson random forcing

    Bakhtin, Y., 2013, In : Annals of Probability. 41, 4, p. 2961-2989 29 p.

    Research output: Contribution to journal › Article

    Global Minimizer
    Burgers Equation
    Forcing
    Siméon Denis Poisson
    Existence and Uniqueness
    2012

    A neural computation model for decision-making times

    Bakhtin, Y. & Correll, J., Oct 2012, In : Journal of Mathematical Psychology. 56, 5, p. 333-340 8 p.

    Research output: Contribution to journal › Article

    Decision Making
    Decision making
    Noise
    Exit Time
    Reaction Time

    Decision Making Times in Mean-Field Dynamic Ising Model

    Bakhtin, Y., Jul 2012, In : Annales Henri Poincare. 13, 5, p. 1291-1303 13 p.

    Research output: Contribution to journal › Article

    decision making
    Mean Field
    Ising model
    Ising Model
    Dynamic Model

    Invariant densities for dynamical systems with random switching

    Bakhtin, Y. & Hurth, T., Oct 2012, In : Nonlinearity. 25, 10, p. 2937-2952 16 p.

    Research output: Contribution to journal › Article

    Hypoellipticity
    Random Dynamical Systems
    Nonautonomous Differential Equations
    Absolute Continuity
    Smooth Manifold
    2011

    Noisy heteroclinic networks

    Bakhtin, Y., Jun 2011, In : Probability Theory and Related Fields. 150, 1-2, p. 1-42 42 p.

    Research output: Contribution to journal › Article

    Precise Asymptotics
    Heteroclinic Orbit
    Jump Process
    Rescaling
    Saddlepoint

    Normal forms approach to diffusion near hyperbolic equilibria

    Monter, S. A. A. & Bakhtin, Y., Jun 2011, In : Nonlinearity. 24, 6, p. 1883-1907 25 p.

    Research output: Contribution to journal › Article

    Scaling Limit
    White noise
    Normal Form
    Dynamical systems
    Exit Problem

    Scaling limit for the diffusion exit problem in the Levinson case

    Monter, S. A. A. & Bakhtin, Y., Jan 2011, In : Stochastic Processes and their Applications. 121, 1, p. 24-37 14 p.

    Research output: Contribution to journal › Article

    Exit Problem
    Exit Time
    Scaling Limit
    Diffusion Problem
    Dynamical systems

    SPDE approximation for random trees

    Bakhtin, Y., 2011, In : Markov Processes and Related Fields. 17, 1, p. 1-36

    Research output: Contribution to journal › Article

    The Optimal Sink and the Best Source in a Markov Chain

    Bakhtin, Y. & Bunimovich, L., Jun 2011, In : Journal of Statistical Physics. 143, 5, p. 943-954 12 p.

    Research output: Contribution to journal › Article

    Markov chains
    sinks
    Markov chain
    Hitting Time
    stopping
    2010

    Localization and perron-frobenius theory for directed polymers

    Bakhtin, Y. & Khanin, K., 2010, In : Moscow Mathematical Journal. 10, 4, p. 667-686 20 p.

    Research output: Contribution to journal › Article

    Perron-Frobenius Theory
    Directed Polymers
    Random Potential
    Cocycle
    Path

    Poisson limit for associated random fields

    Bakhtin, Y., 2010, In : Theory of Probability and its Applications. 54, 4, p. 678-681 4 p.

    Research output: Contribution to journal › Article

    Poisson Point Process
    Rescaling
    Random Field
    Siméon Denis Poisson
    Converge

    Small noise limit for diffusions near heteroclinic networks

    Bakhtin, Y., Sep 2010, In : Dynamical Systems. 25, 3, p. 413-431 19 p.

    Research output: Contribution to journal › Article

    Dynamical systems
    Stochastic Calculus
    Random Perturbation
    Probability Theory
    Dynamical system

    Solutions of semilinear wave equation via stochastic cascades

    Bakhtin, Y. & Mueller, C., 2010, In : Communications on Stochastic Analysis. 4, 3, p. 425-431

    Research output: Contribution to journal › Article

    Thermodynamic limit for large random trees

    Bakhtin, Y., Oct 2010, In : Random Structures and Algorithms. 37, 3, p. 312-331 20 p.

    Research output: Contribution to journal › Article

    Random Trees
    Thermodynamic Limit
    Thermodynamics
    Limiting Distribution
    Gibbs Distribution
    2009

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

    Bakhtin, Y. & Heitsch, C. E., Jan 2009, In : Bulletin of Mathematical Biology. 71, 1, p. 84-106 23 p.

    Research output: Contribution to journal › Article

    RNA Secondary Structure
    Random Trees
    secondary structure
    RNA
    Large Deviations
    2008

    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

    Unit tangent vector
    Harmonic Measure
    Hyperbolic Surface
    Lamination
    Tangent Bundle

    Exit asymptotics for small diffusion about an unstable equilibrium

    Bakhtin, Y., May 2008, In : Stochastic Processes and their Applications. 118, 5, p. 839-851 13 p.

    Research output: Contribution to journal › Article

    White noise
    Dynamical systems
    Refinement
    Dynamical system
    Unstable

    Large deviations for random trees

    Bakhtin, Y. & Heitsch, C., Aug 2008, In : Journal of Statistical Physics. 132, 3, p. 551-560 10 p.

    Research output: Contribution to journal › Article

    Random Trees
    Large Deviation Principle
    Large Deviations
    Gibbs Distribution
    deviation

    Self-similar Markov processes on Cantor set

    Bakhtin, Y., Oct 17 2008, In : arXiv. 0810.3260.

    Research output: Contribution to journal › Article

    Markov Semigroups
    Self-similar Processes
    Cantor set
    Markov Process
    Brownian motion
    2007

    Burgers equation with random boundary conditions

    Bakhtin, Y., Jul 2007, In : Proceedings of the American Mathematical Society. 135, 7, p. 2257-2262 6 p.

    Research output: Contribution to journal › Article

    Exponential Convergence
    Existence and Uniqueness Theorem
    Stationary Distribution
    Burgers Equation
    Stationary Solutions

    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

    Malliavin Calculus
    Infinite-dimensional Systems
    Additive Noise
    Stochastic Reaction-diffusion Equations
    Hypoelliptic Operators
    2006

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

    Bakhtin, Y., Jan 2006, In : Journal of Statistical Physics. 122, 2, p. 351-360 10 p.

    Research output: Contribution to journal › Article

    Navier-Stokes System
    uniqueness
    Stationary Solutions
    Forcing
    Cascade

    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

    Stochastic Navier-Stokes Equation
    Random Operators
    Navier-Stokes System
    Stochastic Systems
    Lyapunov Exponent
    2005

    Regularity of solutions to vorticity navier-stokes system on ℝ2

    Arnold, M., Bakhtin, Y. & Dinaburg, E., Sep 2005, In : Communications in Mathematical Physics. 258, 2, p. 339-348 10 p.

    Research output: Contribution to journal › Article

    Navier-Stokes System
    Regularity of Solutions
    regularity
    Vorticity
    vorticity

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

    Bakhtin, Y. & Mattingly, J. C., Oct 2005, In : Communications in Contemporary Mathematics. 7, 5, p. 553-582 30 p.

    Research output: Contribution to journal › Article

    Stochastic Partial Differential Equations
    Lyapunov functions
    Stationary Solutions
    Navier Stokes equations
    Partial differential equations
    2004

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

    Bakhtin, Y., Dinaburg, E. I. & Sinai, Y. G., Nov 2004, In : Russian Mathematical Surveys. 59, 6, p. 1061-1078 18 p.

    Research output: Contribution to journal › Article

    Navier-Stokes System
    Power Law
    Existence and Uniqueness Theorem
    Local Existence
    Energy

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

    Arnol'd, M. D., Bakhtin, Y. & Dinaburg, E. I., May 2004, In : Russian Mathematical Surveys. 59, 3, p. 560-561 2 p.

    Research output: Contribution to journal › Article

    Navier-Stokes System
    Regularity of Solutions
    2003

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

    Bakhtin, Y., 2003, In : Theory of Probability and its Applications. 47, 4, p. 684-688 5 p.

    Research output: Contribution to journal › Article

    Stationary Solutions
    Stochastic Equations
    Existence and Uniqueness
    Differential equation
    Sufficient Conditions
    2002

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

    Bakhtin, Y., 2002, In : Theory of Probability and its Applications. 46, 3, p. 387-405 19 p.

    Research output: Contribution to journal › Article

    Moment Inequalities
    Convergence in Distribution
    Maximal Inequality
    Functional Central Limit Theorem
    Gaussian Fields
    2001

    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