Purdue Probability Seminar, Fall 2026

In work by Hairer, rough path theory is used to construct solutions to the stochastic Burgers type equation and to establish their regularity. In later work by Hairer, Maas, and Weber, the authors prove that spatial discretizations of the equation converge with rate up to 1/6, which is suboptimal. In the talk, I will discuss how these properties are affected when the classical derivative is replaced by fractional derivatives.

We show that the supremum of a canonical process under a given marginal index distribution can be characterized by an integral of the rate-distortion function of the index distribution across various scales. This gives a sharp two-sided version of Dudley's integral by replacing the log covering number by the rate-distortion function from information theory. As applications, we provide new streamlined proofs of the majorizing measure theorem and the Bednorz-Latala theorem (formerly the Bernoulli conjecture). Furthermore, the value of entropic optimal transport can be sharply characterized by a truncated rate-distortion integral. (Based on arXiv:2508.18682, 2604.14061, and 2608.11031).