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The Summer school on "Spectral properties of large random objects" will be held at the Institut des Hautes Etudes Scientifiques (IHES) from July 17 to July 28, 2017. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris).

The school is open to everybody but intended primarily for young participants, including PhD students and postdoctoral fellows.

Studying spectral properties of large random objects has been a very active playground in probability theory, mathematical physics and computer science during the last decades.

The motivations are manifold: viewing random matrices as a model for complicated quantum Hamiltonians, studying random Schrödinger operators to understand the Anderson localization phenomenon, viewing eigenvectors of random matrices as models for eigenmodes of quantized chaotic systems, or understanding the geometry of large (random) graphs such as expanders via the spectral properties of their adjacency matrices. In those studies the emphasis is generally put either on the eigenvalues or the eigenvectors of the object.

The goal of the summer school is to present to the selected students (from master students to postdocs) a panoramic view of this rich area, in order to arouse their interest for some old problems which are coming back on stage, as well as the new exciting horizons of the field.

Some funding is available for young participants (more info at the bottom of the page)

Main courses:

• Charles BORDENAVE (Université de Toulouse) Spectrum of random graphs

• Paul BOURGADE (New York University) Universality and quantum unique ergodicity in random matrix theory

• Frédéric KLOPP (Université Pierre et Marie Curie)
Large systems of interacting quantum particles in a random field

• Eyal LUBETZKY (New York University) Spectral vs. geometric approaches to random walks on random graphs

• Yuval PERES (Microsoft Research) The cutoff phenomenon and rate of escape for Markov chains

• Christophe SABOT (Université de Lyon 1) Self-interacting processes and random Schrödinger operators

• Balint VIRAG (University of Toronto) Operator limits of random matrices

• Simone WARZEL (Technische Universität München)
Topics in random operator theory

Organising Committee:

Nicolas CURIEN (Université Paris-Sud) Hugo DUMINIL-COPIN (IHES) Jean-François LE GALL (Université Paris-Sud) Stéphane NONNENMACHER (Université Paris-Sud)