Asymptotics of Random Matrices and Related Models: The Uses of Dyson-schwinger Equations - Couverture souple

Guionnet, Alice

 
9781470450274: Asymptotics of Random Matrices and Related Models: The Uses of Dyson-schwinger Equations
Couverture souple
ISBN 10 : 1470450275 ISBN 13 : 9781470450274
Editeur : American Mathematical Society, 2019

Synopsis

Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models.

These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Alice Guionnet, Universite de Lyon, CNRS, ENS de Lyon, France.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2019
Langue
anglais
ISBN 10 
1470450275
ISBN 13 
9781470450274
Reliure
Broché
Nombre de pages
144
Coordonnées du fabricant
non disponible
Personne responsable
non disponible