Statistical physics on sparse random graphs: A mathematical perspective
Statistical Physics and Computation: Boltzmann-Gibbs distributions, factor models and Constraint Satisfaction Problems. Average complexity, ground states and sparse random graph ensembles. Locally tree-like graphs, Bethe-Peierls prediction and Belief Propagation equations. Amir DEMBO
Course Description
Theoretical models of disordered materials yield precise predictions about the typical complexity of certain combinatorial optimization problems. The underlying common structure is that of many discrete variables, whose interaction is represented by a random ‘tree like’ sparse graph. I will survey recent progress in proving such predictions, the related insights gained from it, and certain interesting connections with spin-glass models, random matrices and extremal graphs.
-
- Statistical Physics and Computation: Boltzmann-Gibbs distributions, factor models and Constraint Satisfaction Problems. Average complexity, ground states and sparse random graph ensembles. Locally tree-like graphs, Bethe-Peierls prediction and Belief Propagation equations.
-
Amir DEMBO
2016/10/28 1:45:02 英語
-
- Extremal cuts: From Sparse random graphs to spin-glasses.
-
Amir DEMBO
2016/11/01 1:58:28 英語
-
- The ferromagnetic Potts (and Ising) model: Proving replica-symmetric free energy prediction by interpolation and graph decimation.
-
Amir DEMBO
2016/11/08 2:02:02 英語
-
- Non-linear large deviations in counting (sparse) graph homeomorphisms and k-arithmetic progressions.
-
Amir DEMBO
2016/11/11 1:52:10 英語
-
- Gibbs measures, the set of near-optimal solutions for CSP-s and justifying the one Replica-Symmetry-Breaking prediction.
-
Amir DEMBO
2016/11/18 2:06:12 英語
講義詳細
- 年度・期
- 2016年度・後期集中
- 開催日
- 2016年10月28日 から 11月18日
- 開講部局名
- 理学研究科
- 使用言語
- 英語
- 教員／講師名
- Amir DEMBO（Distinguished Visiting Professor, Kyoto University / Professor, Stanford University）
- 開催場所
- Room 127, Graduate School of Science Bldg No 3
