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Asymptotics of random matrices and related models : the uses of Dyson-Schwinger equations

Author: Alice Guionnet; Conference Board of the Mathematical Sciences.; National Science Foundation (U.S.)
Publisher: [Providence, RI] : American Mathematical Society, [2019]
Series: Regional conference series in mathematics, no. 130.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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  Read more...
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Document Type: Book
All Authors / Contributors: Alice Guionnet; Conference Board of the Mathematical Sciences.; National Science Foundation (U.S.)
ISBN: 9781470450274 1470450275
OCLC Number: 1082292762
Notes: "Support from the National Science Foundation."
Description: vii, 143 pages ; 26 cm.
Contents: 1. Introduction --
2. The example of the GUE --
3. Wigner random matrices --
4. Beta-ensembles --
5. Discrete beta-examples --
6. Continuous beta-models : the several cut case --
7. Several matrix-ensembles --
8. Universality for beta-models.
Series Title: Regional conference series in mathematics, no. 130.
Responsibility: Alice Guionnet.

Abstract:

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  Read more...

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