Bøker av Alice Guionnet

Describes 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 shows how these equations are derived, and how to obtain the concentration of measure estimates required to study these equations asymptotically.

This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables.