Spring School

Threshold phenomena and random graphs
Paris, Institut Henri Poincaré (I.H.P.), May 27-31, 2013

This Spring School will consist in two courses given by professors Chatterjee and Kahn on threshold phenomena and random graphs.

• Sourav Chatterjee (Courant Institute, New York University, USA) - Applications of graph limits in probability and statistics.
  The theory of limits of dense graph sequences is a branch of modern graph theory, developed in a series of papers in the last seven years by Laszlo Lovasz and coauthors. This course will introduce the basic components of this theory, and demonstrate its applications to solve previously intractable questions in probability and statistics. The probabilistic application will involve a general large deviation principle for random graphs and its many surprising consequences. The statistical application will center around a certain class of models called “exponential random graph models” (ERGM's) that are becoming increasingly important in the analysis of social networks.
• Jeff Kahn (Rutgers University, USA) - Thresholds.
  Thresholds for increasing properties are a central concern in probabilistic combinatorics and elsewhere. (An increasing property, say F, is a superset-closed family of subsets of some (here finite) set X, and the threshold question for such an F asks, roughly, about how many random elements of X should one choose to make it likely that the resulting set lies in F? For example: about how many random edges from the complete graph Kn are typically required to produce a Hamiltonian cycle?) These lectures will primarily focus on recent progress (and lack thereof) on threshold and related questions. Lecture Notes in PDF: Day1 Day2 Day3 ZIP of HTML files

The school is part of the the A.N.R. project GeMeCoD.

Participation of postdocs and PhD students is strongly encouraged.

Lectures will be held in the main amphitheater (Hermite) of the I.H.P.

Coffee/tea will be available before each slot.

• Accomodations: List of hotels close to the I.H.P.. Young people may find affordable accomodations in fiap and cisp
• Venue: Access map to the I.H.P.
• Lunch: Restaurants located close to the I.H.P.

Djalil Chafaï (Paris-Est), Nathaël Gozlan (Paris-Est), Cyril Roberto (Paris-Ouest), Paul-Marie Samson (Paris-Est)

With the crucial support of Audrey Patout and Christiane Lafargue.

Contact: springschool2013ihp@gmail.com

Institut Henri Poincaré (IHP), A.N.R. projet GeMeCoD, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) - Université de Paris-Est-Marne-la-Vallée (UPEMLV), Institut Universitaire de France (IUF), Labex Bézout, CNRS.

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