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Scaling limits of random walks and their time changes on trees and other graphs

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I will survey some recent work regarding the scaling limits of random walks and the associated local times on trees and other graphs. The models discussed will include critical Galton-Watson trees, the uniform spanning tree in two dimensions and self-similar pre-fractal graphs. I will further describe how, as a consequence of these results, it is possible to understand the scaling limits of some natural time-changes of the random walks, such as the Bouchaud trap model, and also the two common variants of the continuous time random conductance model. The latter results are part of ongoing work with Ben Hambly (Oxford) and Takashi Kumagai (Kyoto).

This talk is part of the Probability series.

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