Log-gases and random matrices. (English) Zbl 1217.82003

London Mathematical Society Monographs Series 34. Princeton, NJ: Princeton University Press (ISBN 978-0-691-12829-0/hbk). xiv, 791 p. (2010).
This monograph develops the theory of solvable log-gases systems in statistical mechanics, with motivations mainly coming from the topics of random matrices, Painlevé systems, stochastic growth processes of Jack polynomials. The presentation aims at being self-contained and develops also the intersection between log-gases and random matrices, with special topics detailed separately. Among others, it includes sections on Selberg functions, Painlevé transcendants, macroscopic electrostatics and circular of Laguerre-Jacobi ensembles.


82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
60B20 Random matrices (probabilistic aspects)