Statistical physics on sparse random graphs: A mathematical perspective
Statistical Physics and Computation: BoltzmannGibbs distributions, factor models and Constraint Satisfaction Problems. Average complexity, ground states and sparse random graph ensembles. Locally treelike graphs, BethePeierls 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 spinglass models, random matrices and extremal graphs.

 Statistical Physics and Computation: BoltzmannGibbs distributions, factor models and Constraint Satisfaction Problems. Average complexity, ground states and sparse random graph ensembles. Locally treelike graphs, BethePeierls prediction and Belief Propagation equations.

Amir DEMBO
Nov. 18, 2016 1:45:02 English

 Extremal cuts: From Sparse random graphs to spinglasses.

Amir DEMBO
Nov. 18, 2016 1:58:28 English

 The ferromagnetic Potts (and Ising) model: Proving replicasymmetric free energy prediction by interpolation and graph decimation.

Amir DEMBO
Nov. 18, 2016 2:02:02 English

 Nonlinear large deviations in counting (sparse) graph homeomorphisms and karithmetic progressions.

Amir DEMBO
Nov. 18, 2016 1:52:10 English

 Gibbs measures, the set of nearoptimal solutions for CSPs and justifying the one ReplicaSymmetryBreaking prediction.

Amir DEMBO
Nov. 18, 2016 2:06:12 English
Details
 Year/Term
 2016 / Intensive, Second semester
 Date
 October 28th to November 18th, 2016
 Faculty/
Graduate School  Graduate School of Science
 Language
 English
 Instructor name
 Amir DEMBO（Distinguished Visiting Professor, Kyoto University / Professor, Stanford University）
 Place
 Room 127, Graduate School of Science Bldg No 3
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