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28/06/2019, 15:00 — 16:00 — Room P3.31, Mathematics Building

Joe Chen, *Colgate University*

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Random walks, electric networks, moving particle lemma, and hydrodynamic limits

While the title of my talk is a riff on the famous monograph *Random walks and electric networks* by Doyle and Snell, the contents of my talk are very much inspired by the book. I'll discuss how the concept of electrical resistance can be applied to the analysis of interacting particle systems on a weighted graph. I will start by summarizing the results of Caputo-Liggett-Richthammer, myself, and Hermon-Salez connecting the many-particle stochastic process to the one-particle random walk process on the level of Dirichlet forms. Then I will explain how to use this type of energy inequality to bound the cost of transporting particles by the effective resistance, and to perform coarse-graining on a class of state spaces which are bounded in the resistance metric. This new method plays a crucial role in the proofs of scaling limits of boundary-driven exclusion processes on the Sierpinski gasket.