{"paper":{"title":"Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Franz Merkl, Margherita Disertori, Silke W.W. Rolles","submitted_at":"2017-10-06T08:21:53Z","abstract_excerpt":"We introduce a family of real random variables $(\\beta,\\theta)$ arising from the supersymmetric nonlinear sigma model and containing the family $\\beta$ introduced by Sabot, Tarr\\`es, 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02308","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}