Probability Seminar

Date: April 2, 2018

Time: 2:00PM - 3:00PM

Location: BLOC 220

Speaker: Eliran Subag, Courant Institute NYU

Title: The geometry of pure states in spherical spin glasses

Abstract: Following Parisi's celebrated replica symmetry breaking solution for mean-field spin glasses (1980), physicists invested considerable efforts to interpret it in terms of `physical' properties of the system. One of the central ideas in their theory was that the system decomposes into `pure states', organized in an ultrametric structure. In his seminal work Talagrand (2010) proved for a wide class of models the existence of such a decomposition -- a sequence of subsets on which the Gibbs measure asymptotically concentrates. Panchenko (2013) established the famous ultrametricity conjecture, which implies, in particular, that those subsets are organized in a certain hierarchical structure. In the context of the spherical models, I will describe a new geometric picture for the above, in which the hierarchy is expressed through a tree of nested spherical bands. In particular, the pure states concentrate on bands corresponding to the leaves of this tree.