Yuri Bakhtin

About

Yuri Bakhtin is a Professor of Mathematics at NYU with research interests in random dynamics and probabilistic models of mathematical physics. His work focuses on the study of stochastic processes and their applications within mathematical physics, contributing to the understanding of complex systems influenced by randomness. Bakhtin's research explores the interplay between probability theory and physical models, advancing the theoretical framework of stochastic dynamics. He is recognized for his contributions to the mathematical understanding of systems governed by randomness, particularly in the context of stochastic homogenization and probabilistic models. His work enhances the comprehension of how random influences affect the behavior of physical and mathematical systems, providing insights into the fundamental nature of stochastic processes in various scientific domains.

Research topics

• Mathematical analysis
• Sociology
• Mathematics
• Statistical physics
• Evolutionary biology
• Geometry
• Genetics
• Biology
• Pure mathematics
• Mathematical optimization

Selected publications

• Localization of directed polymers in continuous space

  Electronic Journal of Probability · 2020 · 20 citations

  1st authorCorresponding

  The first main goal of this article is to give a new metrization of the Mukherjee–Varadhan topology, recently introduced as a translation-invariant compactification of the space of probability measures on Euclidean spaces. This new metrization allows us to achieve our second goal which is to extend the recent program of Bates and Chatterjee on localization for the endpoint distribution of discrete directed polymers to polymers based on general random walks in Euclidean spaces. Following their st…

  PublisherDOI

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

  Proceedings of the National Academy of Sciences · 2021 · 17 citations

  1st authorCorresponding

  , selection coefficient of a mutation), when a new beneficial mutation is fixed in the evolving population, which accordingly moves to a different saddle, or on much rarer occasions from a saddle to a local peak. Phenomenologically, this mode of evolution of a large population resembles punctuated equilibrium (PE) whereby phenotypic changes occur in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but the phenotype does not change substantially…

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• Tails of exit times from unstable equilibria on the line

  Journal of Applied Probability · 2020-06-01 · 7 citations

  articleOpen access1st authorCorresponding

  Abstract For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result proved earlier using heavy machinery from Malliavin calculus. In particular, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits. We also discuss our program on rare transitions in noisy heteroclinic n…

  PublisherOA PDFDOI

• Singularities of Invariant Densities for Random Switching between Two Linear ODEs in 2D

  SIAM Journal on Applied Dynamical Systems · 2021-01-01 · 4 citations

  article1st authorCorresponding

  Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 4 September 2020Accepted: 08 July 2021Published online: 11 October 2021Keywordsrandomly switched ODEs, invariant densities, singularities, integral equationsAMS Subject Headings93E15, 93C30, 37A50, 60J25Publication DataISSN (online): 1536-0040Publisher: Society for Industrial and Applied MathematicsCODEN: sjaday

  PublisherDOI

• Punctuated equilibrium as the default mode of evolution of large populations on fitness landscapes dominated by saddle points in the weak-mutation limit

  bioRxiv (Cold Spring Harbor Laboratory) · 2020-07-20 · 3 citations

  preprintOpen access1st author

  Abstract Punctuated equilibrium is a mode of evolution in which phenetic change occurs in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but no major phenotypic change occurs. Punctuated equilibrium has been originally proposed within the framework of paleobiology, to explain the lack of transitional forms that is typical of the fossil record. Theoretically, punctuated equilibrium has been linked to self-organized criticality (SOC), a model i…

  PublisherOA PDFDOI

Recent grants

• CAREER: Ergodicity and Random Media

  NSF · $446k · 2008–2014

• Asymptotic Problems in Random Dynamics

  NSF · $300k · 2018–2023

• Ergodic Theory of Complex Random Dynamics

  NSF · $150k · 2014–2017

Frequent coauthors

• Liying Li

  University of Toronto

  16 shared

• Hongbin Chen

  14 shared

• Jonathan C. Mattingly

  12 shared

• Zsolt Pajor-Gyulai

  9 shared

• Hong-Bin Chen

  Institut des Hautes Études Scientifiques

  8 shared

• Konstantin Khanin

  8 shared

• Yuri I. Wolf

  National Institutes of Health

  7 shared

• Eugene V. Koonin

  National Center for Biotechnology Information

  7 shared

Education

• Ph.D.

  Moscow State University

  2001

Similar researchers at New York University

• Fedor Bogomolovh-32
• Scott Armstrongh-31
• Paul Bourgadeh-28