Columbia/Stony Brook Probability Day, March 6

11:00AM: Opening Discussion

11:15AM: Talk by Dominik Schmid, “Random walk approximation for the stationary distribution of the open ASEP“

Abstract: We investigate the structure of the stationary distribution of the open asymmetric simple exclusion process. More precisely, we show that the stationary distribution can be well-approximated by random walk measures. Our arguments rely on a recent characterization by Bryc of the stationary distribution as a two-layer Gibbs measure. Based on joint work with Zongrui Yang.

12:00PM: Talk by Hindy Drillick, “Extremal scaling limits for random walks in space-time random environments”
Abstract: In this talk, we will consider random walks in a space-time random environment, which can be thought of as a discrete model for diffusing particles in a time-dependent random medium. We will study the scaling limits of these models in certain moderate deviation scaling regimes and show that they are described by stochastic PDEs. The solutions to these SPDEs are Gaussian processes up to a dimension-dependent critical scale. In d=1 we prove that the critical fluctuations are given by the KPZ equation. In d=2, we conjecture that the scaling limit at criticality is given by the 2d critical stochastic heat flow recently constructed by Caravenna, Sun, and Zygouras. This is based on joint works with Sayan Das and Shalin Parekh.

2:00PM: Talk by Roger Van Peski, “The Gamma-disordered Aztec diamond”
Abstract: The dimer model, i.e. random perfect matchings of a bipartite graph, is a classical object about which much is known. As soon as one biases the probability measure by edge weights which are themselves random, very little is known rigorously, though physicists have studied such models for several decades and made extensive predictions. I will discuss a new integrable model in this class (the Gamma-disordered Aztec diamond) which allows us to prove versions of some of these, and also exhibits surprising relations to integrable polymer models which allow one to port results between the two. Joint work with Maurice Duits (KTH), https://arxiv.org/abs/2512.03033.