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Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. (2019): Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model. In: Alea-Latin American Journal of Probability and Mathematical Statistics, Vol. 16, No. 1: pp. 179-209
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We introduce a family of real random variables (beta, theta) arising from the supersymmetric nonlinear sigma model H-2 vertical bar 2 and containing the family beta introduced by Sabot, Tarres, and Zeng (Sabot et al., 2017) in the context of the vertex-reinforced jump process. Using this family we construct an exponential martingale generalizing the ones considered in Sabot and Zeng (2018+) and Disertori et al. (2017). Moreover, using the full supersymmetric nonlinear sigma model we also construct a generalization of the exponential martingale involving Grassmann variables.