Simple concepts benefit from having a name: "local weak
convergence" formalizes the idea that many random graphs
are locally tree-like, or that weak convergence of point processes
implies convergence of associated geometric graphs.
We describe several more contexts where such convergence arises.
Its deepest use is in attempted rigorizations of the cavity method
in the context of solutions of combinatorial optimization problems
over random data. We illustrate with two such problems, one old and
one new:
(i) TSP on the complete graph with random edge lengths
(ii) maximal flows through

Keywords:

Phase Transition;Computation;Reconstruction

Lecture #10874

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