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arXiv · 1710.02308

Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model

Margherita Disertori·Franz Merkl·Silke W. W. Rolles
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Abstract

We introduce a family of real random variables $(β,θ)$ arising from the supersymmetric nonlinear sigma model and containing the family $β$ introduced by Sabot, Tarrès, and Zeng [STZ17] in the context of the vertex-reinforced jump process. Using this family we construct an exponential martingale generalizing the one considered in [DMR17]. Moreover, using the full supersymmetric nonlinear sigma model we also construct a generalization of the exponential martingale involving Grassmann variables.

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Margherita Disertori, Franz Merkl, Silke W. W. Rolles. 2017-10-06. Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model. https://arxiv.org/abs/1710.02308

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