États de la recherche en matrices aléatoires

Institut Henri Poincaré, Paris – December 1-4, 2014 – Amphi Hermite

Agence Nationale de la Recherche Institut Universitaire de France Société Mathématique de France Institut Henri Poincaré

Welcome to the 2014 edition of the SMF conference series États de la recherche. This 2014 edition is devoted to a state of the art in random matrix theory and some applications such as random growth models and random graph theory. The conference consists in mini-courses for non expert audience including PhD students, and complementary talks.

  • The conference will take place in amphitheater Hermite (venue: IHP, Google Maps).
  • The registration is free but mandatory (see below).
  • A poster is available in PDF.

Eugene Wigner

  • Mini-courses
    • Charles Bordenave (CNRS Toulouse, France) - Spectrum of random graphs.
      The spectral properties of large random graphs attracts a growing attention in various branches of mathematics, computer science and statistical physics of disordered systems. The motivation comes from many distinct directions, notably random matrices, random Schrödinger operators, quantum ergodicity or algorithmic spectral graph theory. In this mini-course, we will present some recent results on eigenvalues and eigenvectors of adjacency matrices of finite graphs and conclude with some open problems. (Lecture Notes)
    • Alexei Borodin (MIT, USA) - Macdonald processes.
      Our goal is to explain how certain basic representation theoretic ideas and constructions encapsulated in the form of Macdonald processes lead to nontrivial asymptotic results in various `integrable' probabilistic problems. Examples include dimer models, general beta random matrix ensembles, and various members of the (2+1)d anisotropic KPZ and (1+1)d KPZ universality classes, such as growing stepped surfaces, q-TASEP, q-PushASEP, and directed polymers in random media. Slides 1/3 Slides 2/3 Slides 3/3
    • Antti Knowles (ETHZ, Switzerland) - Local laws in random matrix theory.
      We will give an introduction to local laws in random matrix theory, focusing on the simple case of Wigner matrices. The first part of the course is devoted to the proof of the local law. In the second part, we will give applications to eigenvector delocalization and the universality of the eigenvalue distribution. If time allows, we will discuss further applications to deformed matrix ensembles.
  • Complementary talks
    • Paul Bourgade (NYU, USA) - From the mesoscopic to microscopic scale in random matrix theory.
      I will review recent techniques to access microscopic statistics from mesoscopic ones, concerning both eigenvalues and eigenvectors of random matrices. Homogenization and the coupling method play a key role. This complements Antti Knowles' mini course: local laws are very useful a priori estimates. Slides
    • Cédric Boutillier (UPMC, France) - Dimers on Rail Yard Graphs.
      We introduce a general model of dimer coverings of certain plane bipartite graphs, which we call rail yard graphs. Using a transfer matrix approach and the celebrated boson-fermion correspondence, the model can be reformulated as a Schur process. We obtain explicit expressions for the partition function and for the inverse Kasteleyn matrix, which yields all dimer correlation functions. Plane partitions, domino tilings of the Aztec diamond and pyramid partitions arise as particular cases of our model. In the scaling limit, the model shows a similar universal behaviour as the one described by Okounkov and Reshetikhin for plane partitions, in connection with distributions appearing in random matrices. This is based on a joint work with Jérémie Bouttier, Guillaume Chapuy, Sylvie Corteel and Sanjay Ramassamy. Slides
    • Mireille Capitaine (CNRS Toulouse, France) - Spectrum of large deformed Hermitian random matrices and Free Probability Theory.
      We show how free probability theory sheds light on the spectrum of large deformed random matrices, and provides a unified understanding of several phenomena. Slides

Schedule Monday 1 Tuesday 2 Wednesday 3 Thursday 4
09:30-11:00 Borodin Knowles Bordenave Bordenave
11:00-11:30 Break Break Break Break
11:30-12:30 Borodin Knowles Bordenave Bordenave
12:30-14:00 Lunch Lunch Lunch Lunch
14:00-15:30 Knowles Borodin 14:00 Bourgade 14:00 Capitaine
15:30-16:00 Break Break 15:00 Break 15:00 Break
16:00-17:00 Knowles Borodin 15:30 Boutillier 15:30 Discussion

Some of the lecture notes were transformed into a book, entitled “Advanced Topics in Random Matrices”, and published in 2018 in the Panoramas et Synthèses book series of the Société Mathématiques de France.

Registration is over.

 #  Participants Affiliation
Benaych-Georges, Florent Université Paris Descartes
Chafaï, Djalil Université Paris-Dauphine
Peche, Sandrine Universié Paris Diderot
Xia, Bo
Raddaoui, Zouhaier Faculty of Science Gabès
Rouault, Alain Université de Versailles-St-Quentin
Darses, Sébastien Aix-Marseille Université
Salim, Adil ENSAE
Banna, Marwa Université Paris-Est Marne-La-Vallée
Attia, Mohamed Jalel Faculté des sciences de Gabès Tunisie
Najim, Jamal Univ. Paris Est Marne La Vallée & CNRS
Lambert, Gaultier KTH
Bun, Joël Université Paris-Sud
Hardy, Adrien Royal Institute of Technology (KTH)
Dubach, Guillaume Courant Institute (NYU)
Dallaporta, Sandrine CMLA, ENS Cachan
Donati-Martin, Catherine Université de Versailles-St-Quentin
Salez, Justin Université Paris Diderot
Cabanal-Duvillard, Thierry MAP5, Université Paris Descartes
Maurel-Segala, Edouard Université Paris-Sud
Maida, Mylene Université Lille 1
Male, Camille CNRS, Université Paris Descartes
Chapon, Francois Université Paul Sabatier
Groux, Benjamin Univ. Versailles-Saint-Quentin-en-Yvelines
Biane, Philippe CNRS
Hachem, Walid CNRS ; LTCI
Butez, Raphaël Université Paris-Dauphine
Kamary, Kaniav Université Paris-Dauphine
Barraquand, Guillaume Université Paris Diderot
Rochet, Jean MAP5
Michaïl, Alkéos MAP5 - Université Paris Descartes
Khorunzhiy, Oleksiy UVSQ
de Tilière, Béatrice Université Pierre et Marie Curie
Jedrzejewski, Franck CEA
Pajor, Alain Université Paris-Est Marne-la-Vallée
Defosseux, Manon Université Paris Descartes
Menard, Laurent Université Paris Ouest
Tikhomirov, Konstantin University of Alberta
Lelarge, Marc INRIA-ENS
Nguyen, Viet Anh Université d'Angers
Guerrero, Prado Ecole des Mines de Saint Etienne
Boutet de Monvel, Anne Universite Paris 7 and IMJ
Augeri, Fanny Université Paul Sabatier Toulouse
Nemish, Yuriy Université Toulouse 3 Paul Sabatier
Liu, Gang Ecole Polytechnique
Vásquez Vivas, Karen Alexandra Université Paris Sud
García Zelada, David Enrique Université Paris Sud
alfano, giusi Politecnico di Torino
Klopp, Olga Université Paris Ouest
Cook, Nicholas UCLA Mathematics Department
Touboul, Jonathan Collège de France
Hermann, Geoffroy Ecole Polytechnique
Lin, Shen Ecole Normale Superieure
Hajej, Ahmed Université Paris Dauphine
Pevzner, Michael Université de Reims
bougerol, philippe UPMC
Dornic, Ivan CEA Saclay
David, Renfrew UCLA
Trinh, Tuan Phong LAGA, Université Paris 13
Blier, Léonard École Normale Supérieure (ENS)
Lemoine, Thibaut Université Pierre et Marie Curie
Mame, Mohamed Nouakchott University
Garcia del Molino, Luis Université Paris 7
Lemaire, Sophie Université Paris-Sud
Pascal, Frédéric Supelec
Elad Altman, Henri Ecole Normale Supérieure
Dornic, Ivan CEA
Féral, Delphine IMB, Université de Bordeaux
Dang, Nguyen-Bac ENS-Lyon/ Polytechnique
Nica, Alexandru University of Waterloo
Scaman, Kevin ENS Cachan - CMLA
Kalogeratos, Argyris CMLA, ENSC
Josuat-Vergès, Matthieu Université de Marne-la-Vallée
Chassaing, Philippe Institut Élie Cartan
Qiu, Yanqi I2M, Université d'Aix-Marseille
Bufetov, Alexander CNRS I2M
Leblé, Thomas LJLL, Paris 6
Couillet, Romain SUPELEC
Legras, Jerome Axiom AI
Moll, Alexander MIT
Le Foll, Yves Paristech ENS Telecom
Eisenbaum, Nathalie CNRS, Université Paris 6
Allez, Romain WIAS Berlin
Dumaz, Laure Université de Cambridge
Fevrier, Maxime Université Paris-Sud
Frankel, Sid Paris-7 labo AO math
Nguyen, Vulan LPMA, Paris 7
Massoulié, Laurent MSR-Inria Joint Centre
Bouttier, Jérémie IPhT, CEA Saclay
Vignat, Christophe Paris Sud
Pal, Anshuman ENS Paris
Benhamou, Anna Université Paris Diderot
Marchal, Philippe CNRS
Ménassé, Clément Université Paris Diderot
Boutillier, Cédric UPMC

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Credits

The photo of Wigner in front of a blackboard is borrowed from http://www.math.ethz.ch/u/felder/Research/RandomMatrices.
The colorful image of the Ginibre ensemble was created by FBG.

Ginibre Ensemble

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