Research Output per year
Research Output 1997 2019
- 1 - 50 out of 58 results
- Publication Year, Title (descending)
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-R121Research 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.). ForthcomingResearch 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. 1-36Research 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. 425-431Research 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. 30-31Research output: Chapter in Book/Report/Conference proceeding › Conference contribution