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Self-interacting random walks and their asymptotic behavior

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I will discuss some joint work with Anna Erschler and Balint Toth, describing certain one-dimensional self-interacting walks on the set of integers, that choose to jump to the right or to the left randomly but influenced by the number of times they have previously jumped along the edges in the finite neighborhood of their current position. After describing the motivation to study such objects (the quest for new natural, continuous and local evolutions of functions that are neither deterministic PDEs nor stochastic PDEs), we will survey a variety of possible asymptotic behaviors (including some where the walks is eventually confined in an interval of arbitrarily large length) and the corresponding phase transitions.

This talk is part of the Probability series.

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