Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations

We prove structure theorems for measures on the discrete cube and on Gaussian space, which provide sufficient conditions for mean-field behavior. These conditions rely on a new notion of complexity for such measures, namely the Gaussian-width of the gradient of the log-density. On the cube {−1, 1} n...

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Veröffentlicht in:	Geometric and functional analysis 2018-12, Vol.28 (6), p.1548-1596
1. Verfasser:	Eldan, Ronen
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Approximation Complexity Gaussian cubes Ising model Linear functions Mathematical analysis Mathematics Mathematics and Statistics Partitions (mathematics) Theorems
Online-Zugang:	Volltext
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