Abstract
We prove polynomial decay of the mixing field of the Vertex Reinforced Jump Process (VRJP) on ${\mathbb {Z}}^{2}$ with bounded conductances. Using [22] we deduce that the VRJP on ${\mathbb {Z}}^{2}$ with any constant conductances is almost surely recurrent. It gives a counterpart of the result of Merkl, Rolles [16] and Sabot, Zeng [22] for the 2-dimensional Edge Reinforced Random Walk.
Citation
Christophe Sabot. "Polynomial localization of the 2D-Vertex Reinforced Jump Process." Electron. Commun. Probab. 26 1 - 9, 2021. https://doi.org/10.1214/20-ECP356
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