I will talk about the joint work carried out in cooperation with Rafał Martynek and Rafał Meller on the problem of estimating positive stochastic processes. In particular, this applies to the hypothesis of the existence of p-small sets formulated by Talagrand in the context of selector processes and its generalization to empirical and infinitely divisible processes. Our work contains a much simpler proof and some extensions of the result of the Park - Pham team, which gave the first combinatorial solution of the Talagrand's conjecture. At the heart of the approach is the idea of fragment previously used to show the "sunflower lemma" and the "Khan-Kalai hypothesis". The obtained results are a breakthrough in the analysis of positive processes, for which there are no good tools to study the properties of sample paths - in the case discussed by us - the mean value of the supremum over the index set.
Identyfikator spotkania: 251 152 4038 Kod: 276466