I am a ARC postdoc at Georgia Tech (formerly a Visiting Assistant Professor of Mathematics)
Office: Klaus 2111
E-mail Address: bernstein [at] math [dot] gatech [dot] edu
My research is in the fields of probability, random algorithms, and combinatorics. This
includes finding Markov chain mixing times, such as for random walks on
the symmetric group
(also known as card shuffles), using tools from
representation theory, algebraic combinatorics, and probability.
- On sampling graphical Markov models. M. Bernstein, P. Tetali. Submitted arxiv
- Cutoff for random to random card shuffle. M. Bernstein, E.
Nestoridi. Submitted arxiv
- A random walk on the symmetric group generated by random
involutions. M. Bernstein. Electronic Journal of Probability (2018) [pdf]
- Likelihood orders for the p-cycle walks on the symmetric group.
M. Bernstein. Electronic Journal of Combinatorics (2018) [pdf]
- Analyzing Boltzmann Samplers for Bose-Einstein Condensates with
Dirichlet Generating Functions. M. Bernstein, M. Fahrbach, D. Randall, Proceedings of ANALCO18 arxiv
- The Mixing Time for a Random Walk on the Symmetric Group
Generated by Random Involutions. M. Bernstein. Proceedings of the 28-th International
Conference on Formal Power Series and Algebraic Combinatorics [pdf]
My thesis under Persi
Random Walks on the Symmetric Group, Likelihood Orders, and Involutions