On H^2|2 Isomorphism theorems and reinforced loop soup

2019/11/20 by Yinshan Chang, Chang, Yinshan, Dang-Zheng Liu +3
Computer Science · Mathematics · #Algorithms and Data Compression #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1911.09036

openalex publication_date 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that supersymmetric (susy) hyperbolic isomorphism theorems that relate Vertex Reinforced Jump Processes and H^2|2 field, introduced in [2] and [3], are annealed version of isomorphism theorems relating Markov processes and Gaussian free field, with the help of a Bayes formula that relates susy hyperbolic field to susy free field. On the other hand, we also prove a BFS-Dynkin's isomorphism theorem for reinforced loop soup. Moreover, we provide yet another proof of BFS-Dynkin's isomorphism for VRJP a la Feynman-Kac.

Related

• Lectures on Isomorphism Theorems
• Reinforced Loop Soup via Wilson's Algorithm
• Restrictions of some reinforced processes to subgraphs
• A supersymmetric approach to martingales related to the vertex-reinforced jump process
• Dynkin's isomorphism without symmetry