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Published on 10 Dec 2024

Reinforced loop soup revisited

The vertex reinforced contrepart of the Markovian loop soup developed by Le Jan is introduced. I will review some basic notions about reinforced processes and susy hyperbolic sigma models, then explain a concrete construction of the so-called reinforced loop soup field via a random process with reinforcement mechanism. As a corollary we obtain the susy hyperbolic version of isomorphism theorems for the loop soup field. This is an ongoing joint work with Yinshan Chang (Sichuan University), Dang-Zheng Liu (University of Science and Technology of China), and Xiaolin Zeng (Université de Strasbourg).