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math.PR2012
Localization of a vertex reinforced random walks on with sub-linear weights
Anne-Laure Basdevant, Bruno Schapira, Arvind Singh
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 charact…
math.PR2012
Localization on 4 sites for Vertex-reinforced random walks on
Anne-Laure Basdevant, Bruno Schapira, Arvind Singh
We characterize non-decreasing weight functions for which the associated one-dimensional vertex reinforced random walk (VRRW) localizes on 4 sites. A phase transition appears for w…