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math.PR2026
Functional Stochastic Localization
Anming Gu, Bobby Shi, Kevin Tian
Eldan's stochastic localization is a probabilistic construction that has proved instrumental to modern breakthroughs in high-dimensional geometry and the design of sampling algorit…
math.PR2026
Perspectives on Stochastic Localization
Bobby Shi, Kevin Tian, Matthew S. Zhang
We survey different perspectives on the stochastic localization process of Eldan, a powerful construction that has had many exciting recent applications in high-dimensional probabi…
math.PR2024
Concentration Inequalities for Sums of Markov Dependent Random Matrices
Joe Neeman, Bobby Shi, Rachel Ward
We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix…