24 citations · 74 across the 10 of their papers we have counts for
13 papers
Kinetic description of scalar conservation laws with Markovian data
Fraydoun Rezakhanlou
We derive a kinetic equation to describe the statistical structure of solutions to scalar conservation laws , with certain Markov initial conditions. When the H…
The random Arnold Conjecture: a new probabilistic Conley-Zehnder Theory for symplectic maps
Álvaro Pelayo, Fraydoun Rezakhanlou
We take the first steps to develop Conley-Zehnder Theory, as conjectured by Arnold, in the world of probability. As far as we know, this paper provides the first probabilistic theo…
Random Tessellations and Gibbsian solutions of Hamilton-Jacobi Equations
Mehdi Ouaki, Fraydoun Rezakhanlou
We pursue two goals in this article. As our first goal, we construct a family of Gibbs like measures on the set of piecewise linear convex functions $g:\mathbb{R}^2…
Scaling Limit of Small Random Perturbation of Dynamical Systems
Fraydoun Rezakhanlou, Insuk Seo
In this article, we prove that a small random perturbation of dynamical system with multiple stable equilibria converges to a Markov chain whose states are neighborhoods of the dee…
Scalar conservation laws with monotone pure-jump Markov initial conditions
David C. Kaspar, Fraydoun Rezakhanlou
In 2010 Menon and Srinivasan published a conjecture for the statistical structure of solutions to scalar conservation laws with certain Markov initial conditions, proposing a k…
Regular Flows for Diffusions with Rough Drifts
Fraydoun Rezakhanlou
According to DiPerna-Lions theory, velocity fields with weak derivatives in spaces possess weakly regular flows. When a velocity field is perturbed by a white noise, the corr…