A supersymmetric approach to martingales related to the\n vertex-reinforced jump process

2015/11/23 by Margherita Disertori, Disertori, Margherita, Franz Merkl +3 · 1 citation
Mathematics · Physics and Astronomy · #60G42 #60G60 (primary) #82B44 (secondary) #Black Holes and Theoretical Physics #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1511.07157

openalex publication_date 2015/11/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Sabot and Zeng have discovered two martingales, one of which played a key\nrole in their investigation of the vertex-reinforced jump process. Starting\nfrom the related supersymmetric hyperbolic sigma model, we give an alternative\nderivation of these two martingales. They turn out to be the first two\ninstances in an infinite hierarchy of martingales, derived from a generating\nfunction.\n

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