Seminar

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Part 1 of the lecture (By Yier Lin) will focus on the interacting particle system, in particular, the exclusion processes. We will start from their definition. Then we will introduce two methods, duality and coupling, and see how they can be applied to classify the class of invariant distributions of the symmetric and asymmetric exclusion process.

Part 2 of the lecture (by Shalin Parekh) will focus on white-noise driven SPDE. We will motivate the area and then focus on four fundamental subjects: construction of the stochastic calculus for space time white noise, basic linear SPDE and Duhamel’s principle, multiplicative noise equations and the chaos series expansion, and martingale methods to identify the law of an SPDE. Time permitting, we may also discuss two additional subjects: recent progress on singular SPDE, and convergence to equilibrium in the total variation norm.

Part 3 of the lecture (by Kevin Yang) will discuss the connections between interacting particle systems and SPDEs. We start with the problem of hydrodynamic limits for conserved quantities of interacting particle systems and afterwards introduce SPDEs as a fluctuation theory. We first study the symmetric simple exclusion process and then discuss additional difficulties that arise for more general models, for example when we introduce asymmetry. The relevant SPDEs will be the additive stochastic heat equation and the Kardar-Parisi-Zhang equation.

Part 2: Intro to SPDE 1.56 MB application/pdf

Mini-Course- Interacting Particle Systems and SPDEs