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The University of Chicago Department of Statistics Billingsley Lectures on Probability S. R. S. VARADHAN Courant Institute of Mathematical Sciences New York University Large Deviations with Applications to Random Matrices and Random Graphs THURSDAY, May 31, 2012, at 4:00 PM 133 Eckhart Hall, 5734 S. University Avenue ABSTRACT Title: We will apply large deviation theory to the problem of estimating the probability of having some very large eigenvalues in a random symmetric matrix. As an example we can calculate the probability of a random graph with each edge being on of off independently n 3 with probability p and 1 − p. The number of triangles would be roughly p . We estimate 3 n 3 the probability of large deviations from this i.e. 3 a with a 6= p and answer the question of a graph conditioned to have a significantly different number of triangles would look like. For further information and inquiries about building access for persons with disabilities, please contact Dan Moreau at 773.702.8333 or send him an email at [email protected]. If you wish to subscribe to our email list, please visit the following website: https://lists.uchicago.edu/web/arc/statseminars.
