Statistical physics of random CSPs (tutorial)

Abstract

I will describe recent progress in determination of asymptotic behavior in random constraint satisfaction problems, including the independent set problem on random graphs, random regular NAE-SAT, and random SAT. The results include sharp phase transitions and some understanding of solution geometry, particularly in the setting of the random regular NAE-SAT problem. In this lecture I will survey the physics heuristics, and explain how they lead to combinatorial models for the solution geometry, which form a basis of mathematical approaches to these problems. As time allows, I will discuss some of the mathematical techniques that have been introduced, particularly with regards to solving certain non-convex optimization problems that arise in moment method calculations.