Statistical Physics Approach to Asymptotic Enumeration and Large Deviations in Random Graphs - Part 2

Explore statistical physics methods for solving complex combinatorial problems in this 58-minute lecture from the IAS-PCMI Graduate Summer School. Learn fundamental concepts from statistical physics including Gibbs measures, partition functions, and phase transitions, then discover how tools like cluster expansion, coupling, and Markov chain mixing can be applied to two major combinatorial challenges: 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)). Master the connections between statistical physics and combinatorics without requiring prior physics knowledge, building on probability theory foundations including expectation, variance, central limit theorems, Markov chains, and concentration inequalities. Gain insights into how statistical mechanics principles can provide powerful analytical tools for understanding the behavior of large discrete structures and their probabilistic properties.