Research output

Research output per year 1997 2000 2008 2010 2011 2012 2013 2018 2019 2020 2021 2023

• 62 Article
• 3 Conference contribution
• 1 Other report
• 1 Chapter
• 2 More
  • 1 Chapter (peer-reviewed)
  • 1 Review article

Research output per year

Research output per year

Search results

• 2023

  Joint localization of directed polymers

  Bakhtin, Y. & Dow, D., 2023, In: Electronic Journal of Probability. 28, 109.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Random Walk 100%
  • Joints (Structural Components) 100%
  • Joint Localization 100%
  • Lattices 50%
  • Gaussian Distribution 50%

• Strongly mixing smooth planar vector field without asymptotic directions

  Bakhtin, Y. & Li, L., Mar 1 2023, In: Nonlinearity. 36, 3, p. 1789-1798 10 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Asymptotic Direction 100%
  • Strongly Mixing 100%
  • Planar Vector Fields 100%
  • Vector Field 100%
  • Poisson Point Process 50%
• 2022

  Dynamic polymers: invariant measures and ordering by noise

  Bakhtin, Y. & Chen, H. B., Jun 2022, In: Probability Theory and Related Fields. 183, 1-2, p. 167-227 61 p.

  Research output: Contribution to journal › Article › peer-review

  • Asymptotics 100%
  • Invariant Measure 100%
  • Stochastics 33%
  • Initial Condition 33%
  • Nearest Neighbor 33%

• ERRATUM: MALLIAVIN CALCULUS APPROACH TO LONG EXIT TIMES FROM AN UNSTABLE EQUILIBRIUM

  Bakhtin, Y., Chen, H. B. & Pajor-Gyulai, Z., Aug 2022, In: Annals of Applied Probability. 32, 4, p. 3199-3200 2 p.

  Research output: Contribution to journal › Article › peer-review

  • Cauchy-Schwarz Inequality 100%
  • Markov Inequality 50%
• 2021

  ATYPICAL EXIT EVENTS NEAR A REPELLING EQUILIBRIUM

  Bakhtin, Y. & Chen, H. B., May 2021, In: Annals of Probability. 49, 3, p. 1257-1285 29 p.

  Research output: Contribution to journal › Article › peer-review

  • Probability Theory 100%
  • Exit Event 100%
  • Dynamical System 50%
  • Eigenvalue 50%
  • Vector Field 50%

• Evolution in the weak-mutation limit: Stasis periods punctuated by fast transitions between saddle points on the fitness landscape

  Bakhtin, Y., Katsnelson, M. I., Wolf, Y. I. & Koonin, E. V., Jan 26 2021, In: Proceedings of the National Academy of Sciences of the United States of America. 118, 4, e2015665118.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Weak mutation 100%
  • Punctuated Equilibrium 100%
  • Effective Population Size 100%
  • Beneficial Mutation 50%
  • Local Peak 25%

• Long exit times near a repelling equilibrium

  Bakhtin, Y. & Chen, H. B., Apr 2021, In: Annals of Applied Probability. 31, 2, p. 594-624 31 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Exit Time 100%
  • Probability Theory 50%
  • Asymptotics 50%
  • Critical Point 50%
  • Polynomial 50%

• Singularities of invariant densities for random switching between two linear ODEs in 2D

  Bakhtin, Y., Hurth, T., Lawley, S. D. & Mattingly, J. C., 2021, In: SIAM Journal on Applied Dynamical Systems. 20, 4, p. 1917-1958 42 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Dynamical System 100%
  • Vector Field 100%
  • Ordinary Differential Equation 100%
  • Boundedness 100%
  • Fixed Points 100%
• 2020

  Analysis of Attack Actions on the Railway Infrastructure Based on the Integrated Model

  Levshun, D., Bakhtin, Y., Chechulin, A. & Kotenko, I., 2020, Mobile Internet Security - 4th International Symposium, MobiSec 2019, Revised Selected Papers. You, I., Chen, H.-C., Leu, F.-Y. & Kotenko, I. (eds.). Springer Science and Business Media Deutschland GmbH, p. 145-162 18 p. (Communications in Computer and Information Science; vol. 1121).

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

  • Attack Actions 100%
  • Attack Action 100%
  • Multi-step Attack 25%
  • Critical Infrastructure Security 25%
  • Effective Analysis 25%

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

  Bakhtin, Y. & Gaál, A., Aug 1 2020, In: Stochastics and Dynamics. 20, 4, 2050026.

  Research output: Contribution to journal › Article › peer-review

  • Asymptotics 100%
  • Dynamical System 100%
  • Exit Time 100%
  • Dimensional System 50%
  • Universality Class 50%

• Localization of directed polymers in continuous space

  Bakhtin, Y. & Seo, D., 2020, In: Electronic Journal of Probability. 25, p. 1-56 56 p., 142.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Mukherjee 100%
  • Atomicity 100%
  • Unique Element 100%
  • Distribution Update 66%
  • Distributional Fixed Point 66%

• Tails of exit times from unstable equilibria on the line

  Bakhtin, Y. & Pajor-Gyulai, Z., Jun 1 2020, In: Journal of Applied Probability. 57, 2, p. 477-496 20 p.

  Research output: Contribution to journal › Article › peer-review

  • Exit Time 100%
  • Unstable Equilibrium 100%
  • Vector Field 50%
  • Elementary Proof 50%
  • Heteroclinic Connections 50%

• Weakly mixing smooth planar vector field without asymptotic directions

  Bakhtin, Y. & Li, L., Nov 2020, In: Proceedings of the American Mathematical Society. 148, 11, p. 4733-4744 12 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Planar Vector Fields 100%
  • Limiting Direction 33%
  • Random Vector Field 33%
  • Positive Quadrant 33%
• 2019

  Malliavin calculus approach to long exit times from an unstable equilibrium

  Bakhtin, Y. & Pajor-Gyulai, Z., Apr 2019, In: Annals of Applied Probability. 29, 2, p. 827-850 24 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Exit Time 100%
  • Unstable Equilibrium 100%
  • Malliavin Calculus 100%
  • Vector Field 50%
  • Exit Distribution 50%

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

  Bakhtin, Y. & Pajor-Gyulai, Z., Jun 1 2019, In: Stochastics and Dynamics. 19, 3, 1950022.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Scaling Limit 100%
  • Jordan Block 100%
  • Nontrivial Jordan Block 100%
  • Unstable Equilibrium 100%
  • Dynamical System 50%

• 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 › peer-review

  Open Access

  • Asymptotics 100%
  • Thermodynamic Limit 100%
  • Stationary Solution 100%
  • Random Walk 33%
  • Initial Condition 33%

• Transversal fluctuations for a first passage percolation model

  Bakhtin, Y. & Wu, W., May 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 › peer-review

  Open Access

  • Percolation Model 100%
  • First Passage Percolation 100%
  • Transversal 100%
  • Transversals 100%
  • Bounded below 33%

• 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 › peer-review

  • Statistics 100%
  • Diffusion Model 100%
  • Incubation Period 100%
  • Gaussian Distribution 100%
  • Reaction Time 100%
• 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 › peer-review

  • Random Boundary 100%
  • Bounded Variation Solution 50%
  • Pressureless Euler Equations 50%
  • Novel Formula 50%
  • Schwarzschild 33%

• 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 › peer-review

  Open Access

  • Hamilton-Jacobi Equation 100%
  • Global Solution 100%
  • KPZ Universality Class 100%
  • KPZ Scaling 50%
  • Quadratic Hamiltonian 50%

• 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 › peer-review

  Open Access

  • Integration by Part 100%
  • Integration by Parts Formula 33%

• 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 › peer-review

  • Stochastics 100%
  • Global Solution 100%
  • Temperature Limit 100%
  • Stationary Solution 100%
  • Polymer Measure 100%
• 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 › peer-review

  Open Access

  • Noncompact 100%
  • Kick 100%
  • Hyperbolicity 100%
  • Inviscid Burgers Equation 100%
  • Subsequence 50%

• 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 › peer-review

  Open Access

  • Scaling Limit 100%
  • Exit Conditions 100%
  • Conditioned Diffusion 100%
  • Nonlinear Elliptic Equations 100%
  • H-transform 100%
• 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) › peer-review

• 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 › peer-review

  Open Access

  • Critical Point 100%
  • 1D Systems 100%
  • Asymptotics 50%
  • Invariant Measure 50%
  • Dimensional Dynamical System 50%
• 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 › peer-review

  • Noncompact 100%
  • Kick 100%
  • Hyperbolicity 100%
  • Inviscid Burgers Equation 100%
  • Subsequence 50%
• 2013

  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

  • Stochastics 100%
  • Large Deviation Principle 50%
  • Laws of Large Number 50%
  • Scaling Limit 50%
  • Nearest Neighbor 50%

• Gumbel distribution in exit problems

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

  Research output: Contribution to journal › Article › peer-review

  • Gumbel 100%
  • Gumbel Distribution 100%

• 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 › peer-review

  • Asymptotics 100%
  • Scaling Limit 100%
  • Conditionals 100%
  • Nonlinear Elliptic Equation 100%
  • Doob H-transform 100%

• 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 › peer-review

  Open Access

  • Minimizing Curves 100%
  • Stationary Solution 100%
  • Fields of Action 66%
  • Poisson Point 50%
  • Unique Global Solution 33%

• 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 › peer-review

  • Periodic Forcing 100%
  • Ergodic Component 100%
  • Diffusion Behavior 100%
  • Random Force 100%
• 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 › peer-review

  • Neural Computation 100%
  • Decision-Making 100%
  • Distribution Shape 50%
  • Exit Time Distribution 50%
  • Choice Decision 50%

• 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 › peer-review

  • Stable Equilibrium Point 100%
  • Dynamic Ising Model 100%
  • Unstable Approach 100%
  • Mean-field Dynamics 100%
  • Stable Equilibrium 50%

• 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 › peer-review

  Open Access

  • Random Dynamical Systems 100%
  • Nonautonomous Ordinary Differential Equations 100%
  • Absolute Continuity 100%
  • Invariant Density 100%
  • Hypoellipticity 100%
• 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 › peer-review

  • Asymptotics 100%
  • Saddle Point 100%
  • Starting Point 100%
  • Exit Measure 50%
  • Precise Asymptotics 50%

• 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 › peer-review

  Open Access

  • Hyperbolic Equilibrium Point 100%
  • Joints (Structural Components) 100%
  • Intensity Noise 100%
  • Critical Point 100%
  • Initial Condition 100%

• 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 › peer-review

  • Scaling Limit 100%
  • Dynamical System 66%
  • Exit Time 66%
  • Initial Condition 33%
  • Asymptotics 33%

• 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 › peer-review

• 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 › peer-review

  • Initial Distribution 100%
  • Tail Distribution 50%
  • Signal Words 50%
  • Convergence to Equilibrium 50%
  • Irreducible Markov Chain 50%
• 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 › peer-review

  • Perron-Frobenius Theory 100%
  • Strong Maximum 50%
  • Bounded Time Interval 50%
  • Infinite-volume Gibbs Measure 25%
  • Pullback Attractor 25%

• 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 › peer-review

  Open Access

  • Random Field 100%
  • Poisson Limit 100%
  • Poisson Point Process 50%

• 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 › peer-review

  • Small Noise Limit 100%
  • Heteroclinic Connections 100%
  • Stochastic Calculus 100%
  • 2,5-Dimethoxy-4-iodoamphetamine 100%
  • Dynamical System 100%

• 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 › peer-review

• 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 › peer-review

  Open Access

  • Limiting Distribution 100%
  • Random Tree 100%
  • Thermodynamic Limit 100%
  • Limit Theorems 50%
  • Gibbs Distribution 50%
• 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 › peer-review

  Open Access

  • Explicit Rate 100%
  • Plane Trees 100%
  • Combinatorial Model 100%
  • Degree Distribution 100%
• 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 › peer-review

  • Harmonic Measure 100%
  • Riemann Surface 100%
  • Hyperbolic Riemann Surface 100%
  • Probability Measure 50%
  • Tangent Bundle 50%

• 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 › peer-review

  • Unstable Fixed Point 100%
  • Small Diffusion 100%
  • Unstable Equilibrium 100%
  • Asymptotics 100%
  • Dynamical System 50%

• 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 › peer-review

  Open Access

  • Random Tree 100%
  • Vertex Degree 66%
  • Secondary Structure 50%
  • Gibbs Distribution 50%
  • RNA Secondary Structure 33%

• Self-similar Markov processes on Cantor set

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

  Research output: Contribution to journal › Article › peer-review

  • Markov Process 100%
  • Cantor Set 100%
  • Self-similar Markov Processes 100%
  • Brownian Motion 50%
  • Asymptotics 50%