English

On $H^{2|2}$ Isomorphism theorems and reinforced loop soup

Probability 2020-04-22 v2

Abstract

We show that supersymmetric (susy) hyperbolic isomorphism theorems that relate Vertex Reinforced Jump Processes and H22H^{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.

Cite

@article{arxiv.1911.09036,
  title  = {On $H^{2|2}$ Isomorphism theorems and reinforced loop soup},
  author = {Yinshan Chang and Dang-Zheng Liu and Xiaolin Zeng},
  journal= {arXiv preprint arXiv:1911.09036},
  year   = {2020}
}

Comments

16 pages

R2 v1 2026-06-23T12:22:31.721Z