Visiting Speaker
Yufei Zhao
Assistant Professor of Mathematics at Massachusetts Institute of Technology
Large Deviations and Exponential Random Graphs
May 3, 2018
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2:00 pm
177 Huntington Ave
11th floor
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In the exponential random graph model, one samples an n-vertex random graph G with probability proportional to exp(f(G)), where f(G) is some graph parameter. 

The large deviation problem asks for the asymptotics of the log-probaiblity of the rare event that, for a binomial random graph G, some graph parameter f(G) (such as the number of triangles in G) exceeds its expectation, say, by a constant factor.

These two problems are intimately related to each other, and both are quite difficult in general to analyze rigorously. Many problems are open, for instance, the structure of a "typical" instance of an exponential random graph is not known in most cases (though we have solutions in some special cases). I will survey some recent progress, in particular highlighting recent works of Chatterjee, Varadhan, Diaconis, Dembo, and Eldan on the development of new techniques for estimating the partition function of an exponential random graph model and its applications to large deviations estimation.

about the speaker
Yufei Zhao is Assistant Professor of Mathematics at Massachusetts Institute of Technology, where he also received his PhD in 2015. His research focuses on combinatorics and graph theory, and he is particularly interested in understanding randomness and pseudorandomness of discrete systems.

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