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Thursday, October 03, 2024
4:00 PM - 5:00 PM

LA Probability Forum

The scaling limit of the colored asymmetric simple exclusion process
Milind Hegde, Department of Mathematics, Columbia University,

UCLA, Math Sciences, Rm 6627

In the colored asymmetric simple exclusion process, one places a particle of "color" -k at each integer site k ∈ \Z. Particles attempt to swap places with an adjacent particle: at rate q ∈ [0,1) if they are initially ordered (e.g., 1 then 2) and at rate 1 if ordered in reverse (e.g., 2 then 1); thus the particles tend to get more ordered over time. We will discuss the scaling limit of this process, which lies in the Kardar-Parisi-Zhang universality class. It  is given by the directed landscape, which was first constructed in 2018 by Dauvergne-Ortmann-Virág as limits in a very different setting---of fluctuations of a model of a random directed metric. The Yang-Baxter equation and line ensembles (collections of random non-intersecting curves) with certain Gibbs or spatial Markov properties will play fundamental roles in our discussion. This is based on joint work with Amol Aggarwal and Ivan Corwin.

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