Statistical Physics Approach to Asymptotic Enumeration and Large Deviations in Random Graphs - Part 4

Explore statistical physics methods for asymptotic enumeration and large deviations in random graphs in this fourth lecture of a comprehensive series. Learn fundamental statistical physics concepts including Gibbs measures, partition functions, and phase transitions, then discover how tools from statistical physics and algorithms such as cluster expansion, coupling, and Markov chain mixing can be applied to solve complex combinatorial problems. Focus on two key areas: asymptotic enumeration of combinatorial structures (such as counting triangle-free graphs with specific edge densities) and large deviations in random graphs (including lower-tail large deviation problems for triangles in G(n,p)). Gain practical experience applying these theoretical concepts to real combinatorial challenges while building upon prerequisite knowledge of probability theory including expectation, variance, central limit theorems, Markov chains, and concentration inequalities. Benefit from clear explanations that require no prior statistical physics background, making advanced mathematical concepts accessible through expert instruction from Georgia Tech's Will Perkins at the IAS-PCMI summer graduate program focused on probabilistic and extremal combinatorics.