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Diffusions in random environment

Guillaume Barraquand (Laboratoire de Physique, ENS Paris)
When Jun 25, 2020
from 02:30 PM to 03:30 PM
Where Amphithéâtre E
Attendees Guillaume Barraquand
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Jeudi 25 Juin

 

Title:  Diffusions in random environment

Guillaume Barraquand (Laboratoire de Physique, ENS Paris)

 

Abstract: 

Consider the simple random walk on Z. What happens if transition probabilities are themselves random variables independent at each time and each location? Using a Bethe ansatz solvable model, a random walk with Beta distributed transition probabilities, we will see that the extreme behavior of many random walks in the same environment is governed by scalings and statistics that arise in random matrix theory and the Kardar-Parisi-Zhang universality class. Then we will see that the relevant continuous limit of the model is a stochastic flow, introduced by Le Jan-Raimond and partly motivated by models of turbulence. Several diffusions following this stochastic flow behave as Brownian motions with a local attractive interaction called sticky Brownian motions. This talk is based on joint works with Ivan Corwin, Mark Rychnovsky and Pierre Le Doussal.