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