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Look Inside Random Matrix Theory, Interacting Particle Systems, and Integrable Systems

Random Matrix Theory, Interacting Particle Systems, and Integrable Systems

£84.99

Part of Mathematical Sciences Research Institute Publications

Gernot Akemann, Michael Phillips, Jinho Baik, Dong Wang, Pavel Bleher, Karl Liechty, Alexei Borodin, Tom Claeys, Tamara Grava, Percy Deift, Alexander Its, Igor Krasovsky, Maurice Duits, Arno B. J. Kuijlaars, Man Yue Mo, Nicholas M. Ercolani, Peter Forrester, Josselin Garnier, Knut Solna, John Harnad, Alexander Orlov, Doron Lubinsky, Mylene Maida, Jonathan Novak, Neil O'Connell, Christian Pfrang, Govind Menon, Jeremy Quastel, Tomohiro Sasamoto, Mariya Shcherbina, Herbert Spohn, Kazamasa Takeuchi, Terence Tao, Van Vu
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  • Date Published: March 2015
  • availability: Available
  • format: Hardback
  • isbn: 9781107079922

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About the Authors
  • Random matrix theory is at the intersection of linear algebra, probability theory and integrable systems, and has a wide range of applications in physics, engineering, multivariate statistics and beyond. This volume is based on a Fall 2010 MSRI program which generated the solution of long-standing questions on universalities of Wigner matrices and beta-ensembles and opened new research directions especially in relation to the KPZ universality class of interacting particle systems and low-rank perturbations. The book contains review articles and research contributions on all these topics, in addition to other core aspects of random matrix theory such as integrability and free probability theory. It will give both established and new researchers insights into the most recent advances in the field and the connections among many subfields.

    • Contains both a mix of review and original articles from distinguished mathematicians such as Alexei Borodin, Percy Deift, Terence Tao and Van Vu
    • Examines research contributions on long-standing questions from an active field of research
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    Product details

    • Date Published: March 2015
    • format: Hardback
    • isbn: 9781107079922
    • length: 540 pages
    • dimensions: 234 x 30 x 156 mm
    • weight: 0.93kg
    • availability: Available
  • Table of Contents

    Preface
    1. Universality conjecture for all Airy, sine and Bessel kernels in the complex plane Gernot Akemann and Michael Phillips
    2. On a relationship between high rank cases and rank one cases of Hermitian random matrix models with external source Jinho Baik and Dong Wang
    3. Riemann–Hilbert approach to the six-vertex model Pavel Bleher and Karl Liechty
    4. CLT for spectra of submatrices of Wigner random matrices, II: stochastic evolution Alexei Borodin
    5. Critical asymptotic behavior for the Korteweg–de Vries equation and in random matrix theory Tom Claeys and Tamara Grava
    6. On the asymptotics of a Toeplitz determinant with singularities Percy Deift, Alexander Its and Igor Krasovsky
    7. Asymptotic analysis of the two-matrix model with a quartic potential Maurice Duits, Arno B. J. Kuijlaars and Man Yue Mo
    8. Conservation laws of random matrix theory Nicholas M. Ercolani
    9. Asymptotics of spacing distributions fifty years later Peter Forrester
    10. Applications of random matrix theory for sensor array imaging with measurement noise Josselin Garnier and Knut Solna
    11. Convolution symmetries of integrable hierarchies, matrix models and τ-functions John Harnad and Alexander Orlov
    12. Universality limits via 'old style' analysis Doron Lubinsky
    13. Fluctuations and large deviations of some perturbed random matrices Mylene Maida
    14. Three lectures on free probability Jonathan Novak
    15. Whittaker functions and related stochastic processes Neil O'Connell
    16. How long does it take to compute the eigenvalues of a random symmetric matrix? Christian Pfrang, Percy Deift and Govind Menon
    17. Exact solutions of the Kardar–Parisi–Zhang equation and weak universality for directed random polymers Jeremy Quastel
    18. Replica analysis of the one-dimensional KPZ equation Tomohiro Sasamoto
    19. Asymptotic expansions for β matrix models and their applications to the universality conjecture Mariya Shcherbina
    20. KPZ scaling theory and the semidiscrete directed polymer model Herbert Spohn
    21. Experimental realization of Tracy–Widom distributions and beyond: KPZ interfaces in turbulent liquid crystal Kazumasa Takeuchi
    22. Random matrices: the four-moment theorem for Wigner ensembles Terence Tao and Van Vu.

  • Editors

    Percy Deift, New York University, Courant Institute of Mathematical Sciences
    Percy Deift is a professor at the Courant Institute of Mathematical Sciences, New York University. He is the author of Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach (1999) and was elected to the US National Academy of Sciences in 2009.

    Peter Forrester, University of Melbourne
    Peter J. Forrester is a professor in the Department of Mathematics and Statistics at the University of Melbourne, Victoria. He is the author of Log-Gases and Random Matrices (2010) and was elected to the Australian Academy of Science in 2004.

    Contributors

    Gernot Akemann, Michael Phillips, Jinho Baik, Dong Wang, Pavel Bleher, Karl Liechty, Alexei Borodin, Tom Claeys, Tamara Grava, Percy Deift, Alexander Its, Igor Krasovsky, Maurice Duits, Arno B. J. Kuijlaars, Man Yue Mo, Nicholas M. Ercolani, Peter Forrester, Josselin Garnier, Knut Solna, John Harnad, Alexander Orlov, Doron Lubinsky, Mylene Maida, Jonathan Novak, Neil O'Connell, Christian Pfrang, Govind Menon, Jeremy Quastel, Tomohiro Sasamoto, Mariya Shcherbina, Herbert Spohn, Kazamasa Takeuchi, Terence Tao, Van Vu

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