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

Yinshan Chang; Dang-Zheng Liu; Xiaolin Zeng

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arXiv · 1911.09036

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

Yinshan Chang·Dang-Zheng Liu·Xiaolin Zeng

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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.

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Yinshan Chang, Dang-Zheng Liu, Xiaolin Zeng. 2019-11-20. On $H^{2|2}$ Isomorphism theorems and reinforced loop soup. https://arxiv.org/abs/1911.09036

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