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arXiv · 2401.04366

Strongly vertex-reinforced jump process on graphs with bounded degree

Andrea Collevecchio·Tuan-Minh Nguyen
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Abstract

We study asymptotic behaviours of a non-linear vertex-reinforced jump process defined on an arbitrary infinite graph with bounded degree. We prove that if the reinforcement function $w$ is reciprocally integrable and non-decreasing, then the process visits only a finite number of vertices. In the case where $w$ is approximately equal to a super-linear polynomial, we show that the process eventually gets stuck on a star-shaped subgraph and there is exactly one vertex with unbounded local time.

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Andrea Collevecchio, Tuan-Minh Nguyen. 2024-01-09. Strongly vertex-reinforced jump process on graphs with bounded degree. https://arxiv.org/abs/2401.04366

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