Course on spin glasses

開催日時: 
2015/02/24 Tue 10:00 - 12:00
2015/03/11 Wed 10:00 - 12:00
2015/03/19 Thu 15:00 - 17:00
2015/03/23 Mon 15:00 - 17:00
2015/03/25 Wed 13:15 - 15:15
講演者: 
Erwin Bolthausen
講演者所属: 
Kyoto University and University of Zürich
概要: 

 
日時・場所:京都大学理学部 3号館
1回目:2月24日(火) 10:00--12:00 [552教室]
2回目:3月11日(水) 10:00--12:00 [127大会議室]
3回目:3月19日(木) 15:00--17:00 [127大会議室]
4回目:3月23日(月) 15:00--17:00 [127大会議室]
5回目:3月25日(水) 13:15--15:15 [552教室]【このあと関西確率論セミナー

Lecture notes [final ver.]

概要:
Lecture 1: Examples of spin glasses: The Sherrington-Kirkpatrick model and the perceptron. Examples from combinatorial optimization. Analysis of the simplest spin glass, the Random Energy Model (REM for short). The Poisson-Dirichlet point process as the limiting object of the REM.

Lecture 2: The Generalized Random Energy Model (GREM). Its limiting object, the Ruelle probability cascades. Time reversal of the Ruelle cascades, the BS-coalescent. The basic invariance properties of the Ruelle cascades and the BS-coalescent.

Lecture 3: Latakos' proof of the replica symmetric solution of the SK-model. Guerra's replica symmetry breaking bound for SK.

Lecture 4: Ultrametricity. Analysis of a simple case, a non-hierarchical version of the GREM. Panchenko's proof of ultrametricity for the SK and other models, based on the Ghirlanda-Guerra identities. His proof of the Parisi formula.

Lecture 5: Either further details of Panchenko's approach, or a discussion of the Thouless-Anderson-Palmer equations (TAP for short) in connection with the cavity approach.