Transience of vertex-reinforced jump processes with long-range jumps
Abstract
We show that the vertex-reinforced jump process on the -dimensional lattice with long-range jumps is transient in any dimension as long as the initial weights do not decay too fast. The main ingredients in the proof are: an analysis of the corresponding random environment on finite boxes, a comparison with a hierarchical model, and the reduction of the hierarchical model to a non-homogeneous effective one-dimensional model. For we also prove transience of the vertex-reinforced jump process with possibly long-range jumps as long as nearest-neighbor weights are large enough.
Keywords
Cite
@article{arxiv.2305.07359,
title = {Transience of vertex-reinforced jump processes with long-range jumps},
author = {Margherita Disertori and Franz Merkl and Silke W. W. Rolles},
journal= {arXiv preprint arXiv:2305.07359},
year = {2025}
}
Comments
23 pages, 3 figures. The previous version has been split in two papers. This paper focuses on the vertex-reinforced jump process, which allowed to simplify some proofs and to strengthen some results