Supervisors

Suitable for

Abstract

Prerequisites:  Probability theory, combinatorics.

 

Background

Xusheng is willing to supervise projects in the areas of sampling algorithms, design and analysis of Markov chains, with a focus on probabilistic and combinatorial methods. An example project could be the analysis of convergence rates for non-reversible Markov chains. Irreversible chains offer both theoretical challenges and practical benefits, providing insights into stochastic dynamics and enabling the design of faster algorithms for sampling and optimization tasks in fields like statistical physics, machine learning. Their analysis, however, presents unique challenges as classical tools like spectral analysis and conductance bounds may not directly apply.

 

Focus

These projects would suit students with a strong mathematical background, particularly those interested in probability theory, combinatorics, and theoretical computer science. Implementation skills can also be useful, as some projects may involve designing algorithms, running simulations, or exploring computational aspects to complement theoretical insights.

 

Method

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.240603