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Bulk universality of general \(\beta\)-ensembles with non-convex potential. (English) Zbl 1278.82032
Summary: We prove the bulk universality of the \(\beta\)-ensembles with non-convex regular analytic potentials for any \(\beta > 0\). This removes the convexity assumption appeared in the earlier work [the authors, “Universality of general \(\beta\)-ensembles”, preprint arxiv:0907.5605 (2011)]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a “convexified measure” so that the local statistics are preserved under this convexification.
©2012 American Institute of Physics

MSC:
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
15B52 Random matrices (algebraic aspects)
60E15 Inequalities; stochastic orderings
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