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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