Scaling limit for amnesic step-reinforced random walks

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• Lucile Laulin (Université Paris X Nanterre)
• Thursday 11 July 2024, 10:15-11:15
• Seminar Room 1, Newton Institute.

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SSDW01 - Self-interacting processes

A step-reinforced random walk is a self-interacting random walk that, at each step, either repeats one of its former steps chosen uniformly or takes a new step independently from its past. We introduce a variation of the step-reinforced random walk with general memory, which can be interpreted as amnesia. Our main purpose is to establish a version of Donsker’s invariance principle for such amnesic step-reinforced random walks in the so-called diffusive regime. While for the standard step-reinforced walk the limit arising is a noise-reinforced Brownian motion, we show that for the amnesic version, the limiting Gaussian process is actually the sum of a noise-reinforced Brownian motion and a Brownian motion, which are a priori dependent. (Joint work with Marco Bertenghi)

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