Statistical physics on sparse random graphs: A mathematical perspective

Non-linear large deviations in counting (sparse) graph homeomorphisms and k-arithmetic progressions. 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.

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