## On gradient complexity of measures on the discrete cube

Ronen Eldan

Weizmann Institute of Science

December 12, 2016

The motivating question for this talk is: What does a sparse Erdős–Rényi 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 Chatterjee-Varadhan which used limit graph theory to answer this question in the dense regime).