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SUMMARY:Scaling limit for amnesic step-reinforced random walks - Lucile La
 ulin (Université Paris X Nanterre)
DTSTART:20240711T091500Z
DTEND:20240711T101500Z
UID:TALK215593@talks.cam.ac.uk
DESCRIPTION:A step-reinforced random walk is a self-interacting random wal
 k that\, at each step\, either repeats one of its former steps chosen unif
 ormly or takes a new step independently from its past. We introduce a vari
 ation of the step-reinforced random walk with general memory\, which can b
 e interpreted as amnesia. Our main purpose is to establish a version of Do
 nsker&rsquo\;s invariance principle for such amnesic step-reinforced rando
 m walks in the so-called diffusive regime. While for the standard step-rei
 nforced walk the limit arising is a noise-reinforced Brownian motion\, we 
 show that for the amnesic version\, the limiting Gaussian process is actua
 lly the sum of a noise-reinforced Brownian motion and a Brownian motion\, 
 which are a priori dependent. (Joint work with Marco Bertenghi)
LOCATION:Seminar Room 1\, Newton Institute
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