Markov chain Monte Carlo (MCMC) algorithms have found an astounding variety of applications, including approximate counting, combinatorial optimization and modeling. One of the richest sources of sampling problems is statistical physics, where the state space of the Markov chain represents the states of a physical system and sampling lends insight into the thermo-dynamic properties of the model. Our primary goals in this research area include: identifying problems amenable to this approach, designing provably efficient local distributed algorithms for these problems; and developing probabilistic arguments for performing the rigorous analysis. For each of these goals, theoretical computer science has benefited greatly from interactions with other disciplines, most notably physics, where concepts like phase transitions have deepened our understanding of order and efficiency. 

Moreover, statistical physics can drive collections of computational agents to perform tasks. We model the dynamics as self-organizing particle systems performing steps of Markov chains through local interactions. The limiting distributions of these chains have distinct equilibrium characteristics that can form the basis for programming collective behavior. In a related direction, we explore methods for wrangling the complexity of non-reversible Markov chain stationary distributions. While our motivation comes in part from the study of non-equilibrium physical systems, the work we propose in property testing of Markov chains and the approximation of their stationary
distributions is more fundamental.