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Local times of Brownian motion indexed by the Brownian tree

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SSDW03 - Geometry, occupation fields, and scaling limits

We consider Brownian motion indexed by the Brownian tree, which arises in a number of asymptotics for discrete models, interacting particle systems or statistical physics models. Local times are defined as the density of the associated occupation  measure. We establish a Markov property for these local times and prove that they satisfy a stochastic differential equation whose coefficients involve the Airy function. This is based in part on a joint work with Ed Perkins.

This talk is part of the Isaac Newton Institute Seminar Series series.

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