Statistical mechanics is that branch of mathematical physics which seeks to explain how macroscopic behaviour can emerge from the interactions between a large number of microscopic particles; in short, to explain how and why the sum is greater than its parts. Due to the complexity of such models, sophisticated computational algorithms are often required in order to make progress. Chief amongst such tools, are Markov-chain Monte Carlo methods. This project will devise, and rigorously analyse, Monte Carlo algorithms for studying discrete/combinatorial models in both equilibrium and non-equilibrium statistical mechanics.
Markov-chain Monte Carlo methods in statistical mechanics
On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model. Journal of Statistical Physics. 170(1), 22-61. doi: 10.1007/s10955-017-1912-x (2018).
The worm process for the Ising model is rapidly mixing. Journal of Statistical Physics. 164(5), 1082-1102. doi: 10.1007/s10955-016-1572-2 (2016).
The worm process for the Ising model is rapidly mixing. NZ Probability Workshop 2016. (2016).