The *-edge-reinforced random walk

• 成果类型: Article
• 署名作者: Bacallado, Sergio; Sabot, Christophe; Tarres, Pierre
• 署名单位: Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-025-01426-0
• 发表日期: 2025-12
• 页码: 795-819
• 关键词: REINFORCED JUMP PROCESS; bayesian-analysis

摘要

We define a linearly reinforced process called the (*)-Edge-Reinforced Random Walk ((*)-ERRW) which can be seen as a Yaglom reversible, hence non-reversible, extension of the Edge-Reinforced Random Walk (ERRW) introduced by Coppersmith and Diaconis in 1986 [4]. This family of processes also generalizes the r-dependent ERRW introduced by Bacallado et al. in 2009 [3]. Under some assumptions on the initial weights, the (*)-ERRW is partially exchangeable in the sense of Diaconis and Freedman [5], and thus it is a random walk in a random environment. The main result of the paper gives the explicit expression of the mixing law, hence extending the magic formula of Coppersmith and Diaconis from the case of mixtures of reversible Markov chains to the case of mixtures of Yaglom reversible Markov chains.