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Invariant densities for dynamical systems with random switching

- Yuri Bakhtin, T. Hurth
- Mathematics
- 26 March 2012

We consider a nonautonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the… Expand

Large Deviations for Random Trees and the Branching of RNA Secondary Structures

- Yuri Bakhtin, Christine E. Heitsch
- MathematicsBulletin of mathematical biology
- 27 March 2008

TLDR

Thermodynamic Limit for Directed Polymers and Stationary Solutions of the Burgers Equation

- Yuri Bakhtin, Liying Li
- MathematicsCommunications on Pure and Applied Mathematics
- 17 July 2016

The first goal of this paper is to prove multiple asymptotic results for a time‐discrete and space‐continuous polymer model of a random walk in a random potential. These results include: existence of… Expand

Noisy heteroclinic networks

- Yuri Bakhtin
- Mathematics
- 23 December 2007

We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distribution in a… Expand

On global solutions of the random Hamilton–Jacobi equations and the KPZ problem

- Yuri Bakhtin, K. Khanin
- Mathematics
- 7 August 2017

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of… Expand

The Burgers equation with Poisson random forcing

- Yuri Bakhtin
- Mathematics
- 26 September 2011

We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove… Expand

On solutions with infinite energy and enstrophy of the Navier-Stokes system

- Yuri Bakhtin, E. Dinaburg, Y. Sinai
- Mathematics
- 31 December 2004

The Cauchy problem is considered for the Navier-Stokes system. Local and global existence and uniqueness theorems are given for initial data whose Fourier transform decays at infinity as a power-law… Expand

Gumbel distribution in exit problems

- Yuri Bakhtin
- Mathematics
- 26 July 2013

We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values.

Inviscid Burgers equation with random kick forcing in noncompact setting

- Yuri Bakhtin
- Mathematics
- 22 June 2014

We develop ergodic theory of the inviscid Burgers equation with random kick forcing in noncompact setting. The results are parallel to those in our recent work on the Burgers equation with Poissonian… Expand

Regularity of invariant densities for 1D systems with random switching

- Yuri Bakhtin, T. Hurth, Jonathan C. Mattingly
- Mathematics
- 20 June 2014

This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical… Expand

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