Universality-based concentration for matrices generated by a Markov chain

par Dr Alexander Van Werde (Universität Münster)

mardi 14 oct. 2025, 14:00 → 15:00 Europe/Paris

Many applications, ranging from the analysis of time series to clustering methods in reinforcement learning, involve high-dimensional random matrices that are generated by a stochastic process. Such settings can be challenging to analyze due to the dependence involved in the process.

 

In this talk, I present a new universality principle for sums of matrices generated by a Markov chain that enables sharp and flexible concentration estimates when combined with recent advances in the Gaussian literature. A key challenge in the proof is that techniques based only on classical cumulants, which have been used by Brailovskaya and Van Handel in a setting with independent summands, fail to produce efficient estimates in our dependent setting. We hence developed a new approach based on Boolean cumulants and a change--of--measure argument. Based on joint work with Jaron Sanders, available at arXiv:2307.11632.