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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 pm

Grigory 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.

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IDEAS Seminar- Greg Terlov: University of North Carolina at Chapel Hill

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Date:
11 Apr
Time:
3:30 pm – 4:30 pm

Venue

125 Hanes Hall
Hanes Hall, Chapel Hill, NC, 27599, United States

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Date:
11 Apr
Time:
3:30 pm - 4:30 pm
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Venue

125 Hanes Hall
Hanes Hall
Chapel Hill, NC 27599 United States
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