Statistical Physics Approach to Asymptotic Enumeration and Large Deviations in Random Graphs - Part 3

Explore the third part of a comprehensive lecture series on applying statistical physics methods to combinatorial problems in random graph theory. Learn how to use fundamental statistical physics concepts including Gibbs measures, partition functions, and phase transitions alongside computational tools like cluster expansion, coupling, and Markov chain mixing to tackle two interconnected mathematical 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)). Discover how these statistical physics approaches provide powerful frameworks for understanding complex combinatorial phenomena without requiring prior knowledge of statistical physics, though familiarity with probability theory concepts including expectation, variance, central limit theorems, Markov chains, and concentration inequalities is recommended. Gain insights into cutting-edge research methods that bridge discrete mathematics, statistical physics, and theoretical computer science through this 58-minute presentation delivered by Will Perkins from Georgia Tech as part of the IAS-PCMI 2025 Graduate Summer School focused on Probabilistic and Extremal Combinatorics.