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

seminario di fisica matematica

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dalle 11:30 alle 12:30


Dipartimento di Matematica e Informatica, aula 1

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Giovedì 17 Settembre, ore 11:30, Aula 1
EMANUELE MINGIONE, Università di Bologna
Multi-species Mean Field Spin Glasses
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.
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