Florent Baudier: Bi-Lipschitz and coarse embeddings of diamond graphs скачать в хорошем качестве

Florent Baudier: Bi-Lipschitz and coarse embeddings of diamond graphs

Since its use in the early 2000s by Brinkman and Charikar regarding a dimension reduction problem, the geometry of finitely-branching diamond graphs has been thoroughly investigated. For instance, in 2009 Johnson and Schechtman gave a new characterization of the class of uniformly convexifiable Banach spaces in terms of the bi-Lipschitz geometry of the 2-branching diamond graphs. This result is part of the Ribe program which asks for purely metric characterizations of local properties of Banach spaces. The speaker and his coauthors obtained an analog result involving a countably branching version of the diamond graphs as part of the Kalton program (a similar program but for asymptotic properties instead). In order to say something interesting about coarse embeddings or finer quantitative problems, one usually seeks metric invariants in the form of Poincaré type inequalities. Eskenazis, Mendel, and Naor following earlier work of Lee and Naor, recently introduced such an invariant that captures the geometry of 2-branching diamonds. In this talk, we will briefiy discuss this local invariant and explain how a new non-standard probabilistic approach to the Kalton program allows us to derive asymptotic metric invariants that capture the geometry of the countably branching diamond graphs.