Localization of a vertex reinforced random walks on \Z with sub-linear weights

2012/07/10 by Anne-Laure Basdevant, Bruno Schapira, Basdevant, Anne-Laure +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1207.2238

Minor modifications

arxiv created 2012/07/17 · arxiv updated 2012/07/18

Abstract

We consider a vertex reinforced random walk on the integer lattice with sub-linear reinforcement. Under some assumptions on the regular variation of the weight function, we characterize whether the walk gets stuck on a finite interval. When this happens, we estimate the size of the localization set. In particular, we show that, for any odd number N larger than or equal to 5, there exists a vertex reinforced random walk which localizes with positive probability on exactly N consecutive sites.

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