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Multi-Particle Processes with Reinforcements

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Abstract

We consider a multi-particle generalization of linear edge-reinforced random walk (ERRW). We observe that in absence of exchangeability, new techniques are needed in order to study the multi-particle model. We describe an unusual coupling construction associated with the two-point edge-reinforced process on ℤ and prove a form of recurrence: the two particles meet infinitely often a.s.

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Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, OR, 97331-4605, USA

    Yevgeniy Kovchegov

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  1. Yevgeniy Kovchegov
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Correspondence to Yevgeniy Kovchegov.

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This research was supported in part by NSF VIGRE Grant DMS 9983726 at UCLA.

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Kovchegov, Y. Multi-Particle Processes with Reinforcements. J Theor Probab 21, 437–448 (2008). https://doi.org/10.1007/s10959-007-0141-7

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  • DOI: https://doi.org/10.1007/s10959-007-0141-7

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