49th Probability Summer School
Saint-Flour (France), 07 - 19 July 2019

Lectures 2019

Nicolas Curien
Université Paris-Sud Orsay (France)
Random discrete surfaces.

These lectures will be an introduction to the study of random discrete surfaces obtained by gluing of polygons along their sides to create 2D surfaces. They include random trees and random planar maps as special cases. Our focus will be on the geometry of those objects (diameter, volume growth, scaling and local limits...) as well as the behavior of statistical mechanics models on them (percolation, simple random walk, self-avoiding random walk...). In order to get understanding of these random discrete surfaces, we will explore them in a "Markovian way" and relate these explorations to one-dimensional random walk processes. This goes under the name of "peeling exploration" in the random planar map theory and can be seen as generalization of the well-known coding processes for random trees (e.g. breadth first or depth first search). We will see that different type of Markovian explorations can yield to different type of information on the surface.

The lectures will contain exercises as well as open problems (some of them accessible) for those eager to learn more.

Elchanan Mossel
Massachusetts Institute of Technology (USA)
Probabilistic aspects of voting, intransitivity and manipulation.

Philippe Rigollet
Massachusetts Institute of Technology (USA)
Statistical optimal transport.

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