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IDEAS Seminar- Greg Terlov: University of North Carolina at Chapel Hill
11 Apr @ 3:30 pm - 4:30 pm
IDEAS Seminar- Greg Terlov: University of North Carolina at Chapel Hill
11 Apr @ 3:30 pm – 4:30 pmGrigory Terlov
Department of Statistics and Operations Research
University of North Carolina at Chapel Hill
Title: Random optimization problems at fixed temperatures
Abstract: We consider a class of disordered mean-field combinatorial optimization problems, focusing on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a general distribution. We prove Central Limit Theorems for the log-partition function, the weight of a typical configuration, and the Gibbs average in both quenched and annealed forms. We also derive quenched Poisson convergence for the size of the intersection of two independent samples, yielding the strong replica symmetry of the model. Applications cover popular models from the literature, such as the Minimal Matching Problem, Traveling Salesman Problem, and Minimal Spanning Tree Problem, on a sequence of deterministic and random dense block graphs of increasing size. Joint work with Partha S. Dey.