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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 journalArticle

    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 journalArticle

    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 journalReview article

    First-passage Percolation
    Exponent
    Fluctuations
    Model
    Estimate
    2018
    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    Inviscid Limit
    Directed Polymers
    Burger equation
    Burgers Equation
    Stationary Solutions
    2016
    Burgers Equation
    Minimizer
    Forcing
    Hyperbolicity
    Ergodic Theory
    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 proceedingChapter (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 journalArticle

    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 journalArticle

    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 proceedingChapter

    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 proceedingChapter

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    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 journalArticle

    Malliavin Calculus
    Infinite-dimensional Systems
    Additive Noise
    Stochastic Reaction-diffusion Equations
    Hypoelliptic Operators
    2006
    Navier-Stokes System
    uniqueness
    Stationary Solutions
    Forcing
    Cascade
    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 journalArticle

    Navier-Stokes System
    Regularity of Solutions
    regularity
    Vorticity
    vorticity
    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 journalArticle

    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 journalArticle

    Navier-Stokes System
    Regularity of Solutions
    2003
    Stationary Solutions
    Stochastic Equations
    Existence and Uniqueness
    Differential equation
    Sufficient Conditions
    2002
    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 proceedingConference contribution