Erwin Bolthausen(UZH)教授 特別講義

SGU Lecture
講演題目: Course on spin glasses
日時・場所: 京都大学 理学部3号館
平成27年2月24日(火) 10:00〜12:00 [552教室]
平成27年3月11日(水) 10:00〜12:00 [127大会議室]
平成27年3月19日(木) 15:00〜17:00 [127大会議室]
平成27年3月23日(月) 15:00〜17:00 [127大会議室]
平成27年3月25日(水) 13:15〜15:15 [552教室]

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.

Lectures 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.

Lectures 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.

主催: 京都大学大学院理学研究科数学・数理解析専攻京都大学数理解析研究所