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### Random walks in Beta random environment

**Mathematical Physics & Probability**

Speaker: | Guillaume Barraquand, Columbia University |

Location: | 2112 MSB |

Start time: | Tue, Oct 13 2015, 4:10PM |

We consider a model of random walks in space-time random environment, with Beta-distributed transition probabilities. This model is exactly solvable, in the sense that the law of the (finite time) position of the walker can be completely characterized by Fredholm determinantal formulas. This enables to prove a limit theorem towards the Tracy-Widom distribution for the second order corrections to the large deviation principle satisfied by the walker, thus extending the scope of KPZ universality to RWRE. We will also discuss a few similar results about degenerations of the model: a first passage percolation model which is the "zero-temperature" limit, and a certain diffusive limit which leads to well-studied stochastic flows. (Work in collaboration with Ivan Corwin).

Note special day.