Local weak convergence of random graphs and networks

• Lecture 1: Definitions and examples.
• Lecture 2: (i) An "elementary" use in a combinatorial optimization problem (table of RDEs); (ii) mean-field model of distance and Frieze's MST theorem.
• Lecture 3: (i) TSP and transportation problem in the mean-field model; a network flow model (graph); (ii) a tractable "complex networks" model.
• Lecture 4: Brief accounts of other uses of LWC; infinite planar graphs; counting quantities associated with a graph; uniform random quadrangulations. (figure 1 and figure 2).

Papers

The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence. [Aldous-Steele]
Asymptotic fringe distributions for general families of random trees. [Aldous]
A Survey of Max-type Recursive Distributional Equations. [Aldous-Bandyopadhyay]
Processes on Unimodular Random Networks. [Aldous-Lyons]
The zeta(2) Limit in the Random Assignment Problem. [Aldous]
Cost-volume relationships for flows through a disordered network. [Aldous]
A Tractable Complex Network Model based on the Stochastic Mean-field Model of Distance. [Aldous]
Recurrence of distributional limits of finite planar graphs. [Benjamini-Schramm]
Asymptotic Enumeration of Spanning Trees, [Lyons]
Counting without sampling. New algorithms for enumeration problems using statistical physics. [Banyopadhyay-Gamarnik]
Local limit of labeled trees and expected volume growth in a random quadrangulation. [Chassaing-Durhuus]

See also slides from talks by Antar Bandyopadhyay