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On Gaussianwidth gradient complexity and meanfield behavior of interacting particle systems and random graphsSeminar: Probability Seminar  November 1  3:104 p.m.  1011 Evans Hall Ronen Eldan, Weizmann Institute of Science The motivating question for this talk is: What does a sparse Erd\"osR\'enyi random graph, conditioned to have twice the number of triangles than the expected number, typically look like? Motivated by this question, In 2014, Chatterjee and Dembo introduced a framework for obtaining Large Deviation Principles (LDP) for nonlinear functions of Bernoulli random variables (this followed an earlier work of ChatterjeeVaradhan which used limit graph theory to answer this question in the dense regime). The aforementioned framework relies on a notion of "low complexity" functions on the discrete cube, defined in terms of the covering numbers of their gradient. The central lemma used in their proof provides a method of estimating the lognormalizing constant $\log \sum_{x \in \{1,1\}^n} e^{f(x)}$ by a corresponding meanfieldfunctional. 5100000000 

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