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 us 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.
This work is in collaboration with Ivan Corwin.
The Probability Seminars are held in Sequoia Hall, Room 200, at 4:30pm on Mondays. Refreshments are served at 4pm in the Lounge on the first floor.