On a Class of Random Walks with Reinforced Memory

Baur, Erich (2020). On a Class of Random Walks with Reinforced Memory Journal of Statistical Physics, 181(3), pp. 772-802. Springer https://doi.org/10.1007/s10955-020-02602-3

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This paper deals with different models of random walks with a reinforced memory of preferential attachment type. We consider extensions of the Elephant Random Walk introduced by Schütz and Trimper (Phys Rev E 70:044510(R), 2004) with stronger reinforcement mechanisms, where, roughly speaking, a step from the past is remembered proportional to some weight and then repeated with probability p. With probability 1 − p, the random walk performs a step independent of the past. The weight of the remembered step is increased by an additive factor b ≥ 0, making it likelier to repeat the step again in the future. A combination of techniques from the theory of urns, branching processes and α-stable processes enables us to discuss the limit behavior of reinforced versions of both the Elephant Random Walk and its α-stable counterpart, the so-called Shark Random Swim introduced by Businger (J Stat Phys 172(3):701–717, 2004). We establish phase transitions, separating subcritical from supercritical regimes.

Item Type:	Journal Article (Original Article)
Division/Institute:	School of Engineering and Computer Science > Institut für Optimierung und Datenanalyse IODA
Name:	Baur, Erich
Subjects:	Q Science > QA Mathematics
ISSN:	1572-9613
Publisher:	Springer
Language:	English
Submitter:	Erich Baur
Date Deposited:	09 Nov 2020 10:54
Last Modified:	09 Nov 2020 10:54
Publisher DOI:	https://doi.org/10.1007/s10955-020-02602-3
ArXiv ID:	1909.04633
Uncontrolled Keywords:	Reinforced random walks, Preferential attachment, Memory, Stable processes, Branching processes, Pólya urns
ARBOR DOI:	10.24451/arbor.12991
URI:	https://arbor.bfh.ch/id/eprint/12991