Wednesday, 30 March 2022 09:49

Eigenvalue Distribution of Large Random Matrices

  • Author(s): Leonid Pastur, Mariya Shcherbina (B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences, Kharkiv, Ukraine)
  • Publisher: AMS
  • Year: 2011

[L. Pastur, M. Shcherbina, Eigenvalue distribution of large random matrices, AMS, Providence, RI, 2011]

Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries).

The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes.

This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.