TRANSIENCE OF VERTEX-REINFORCED JUMP PROCESSES WITH LONG-RANGE JUMPS

• 成果类型: Article
• 署名作者: Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W.
• 署名单位: University of Bonn; University of Bonn; University of Munich; Technical University of Munich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1739
• 发表日期: 2025
• 页码: 1491-1509
• 关键词: walk

摘要

We show that the vertex-reinforced jump process on the d-dimensional lattice with long-range jumps is transient in any dimension d 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 nonhomogeneous effective one-dimensional model. For d >= 3 we also prove transience of the vertex-reinforced jump process with possibly longrange jumps as long as nearest-neighbor weights are large enough.