Multi-species Mean Field Spin Glasses (E. Mingione)

seminario di fisica matematica

Dettagli dell'evento

17/09/2015
dalle 11:30 alle 12:30

Dipartimento di Matematica e Informatica, aula 1

Vincenzo Coscia

Giovedì 17 Settembre, ore 11:30, Aula 1

EMANUELE MINGIONE, Università di Bologna

Multi-species Mean Field Spin Glasses

Abstract:

In the 80's Parisi proposed a solution for the Sherringhton-Kirkpatrick

model which required the introduction of completely new concepts and revealed a

rich mathematical structure. After the work of Guerra, Talagrand and Panchenko,

the so-called Parisi Theory has now a rigorous mathematical background.

In this talk we consider a multi-species version of the Sherringhton-Kirkpatrick mo-

del, where random couplings are independent but not identical distributed. We

introduce a multidimensional version of the Parisi Theory which, under some conve-

xity assumptions, gives a representation for the thermodynamic limit of the pressure.

We discuss the proof of the Guerra's upper bound and the Panchenko's strategy for

the proof of the lower bound.