MA 393: Topics in random discrete structures

Credits: 3:0

Pre-requisites :

1. Sufficient exposure to probability.
2. Familiarity with basic properties of Brownian motion.

Real trees, the Brownian continuum random tree, phase transition in random graphs, scaling limits of discrete combinatorial structures, random maps, the Brownian map and its geometry

Suggested books and references:

1. Jim Pitman, Combinatorial stochastic processes, Lecture Notes in Mathematics, vol. 1875, Springer-Verlag, Berlin (2006)..
2. Jean-François Le Gall, Random trees and applications, Probability Surveys (2005)..
3. Grégory Miermont, Aspects of random maps, Saint-Flour lecture notes (2014)..

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