Papers:

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A random walk on the category of finite abelian p-groups (arxiv preprint)

We study an irreducible Markov chain on the category of finite abelian p-groups, whose stationary measure is the Cohen-Lenstra distribution. This Markov chain arises when one studies the cokernel of a random matrix M, after conditioning on a submatrix of M. We show two surprising facts about this Markov chain. Firstly, it is reversible. Hence, one may regard it is a random walk on finite abelian p-groups. The proof of reversibility also explains the appearance of the Cohen-Lenstra distribution in the context of random matrices. Secondly, we can explicitly determine the spectrum of the infinite transition matrix associated to this Markov chain.

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A dynamic perspective on the universality phenonomenon for random p-adic matrices (in progress)

We use the random walk defined in a previous paper to give a new perspective on the universality phenomenon for random p-adic matrices.

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Random walks on finite abelian p-groups with extra structure (in progress)

We define and study random walks on finite abelian p-groups with extra structure. We consider groups equipped with a perfect symmetric pairing, groups equipped with a perfect anti-symmetric pairing, and groups containing some fixed group B as a subgroup. We define an irreducible, reversible Markov chain on each class of objects, and study their properties. These Markov chains arise naturally in the context of random matrices.

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Recent Talks and Posters:

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Poster: A random walk on the category of finite abelian p-groups. Bernoulli-IMS 11th World Congress in Probability in Statistics (2024) (pdf)

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Talk: A random walk on the category of finite abelian p-groups. Quebec-Maine Number Theory Seminar (2024) (Slides)