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Random Matrix Theory with an External Source

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 19)

DOI: 10.1007/978-981-10-3316-2

ISBN: 978-981-10-3315-5

Publisher: Springer Singapore - Springer Journals

Jan 14, 2017

1 - 10 of 10 Chapters

LitStream

Chapter 1Introduction

Brézin, Edouard; Hikami, Shinobu

Pages: 1 –2

[Random matrix theory is an approach to complex phenomena, such as the energy levels of nuclei, through integrals over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 2Gaussian Means

Brézin, Edouard; Hikami, Shinobu

Pages: 3 –15

[In this chapter we are dealing with the standard GUE matrix integrals in the absence of any external source.]
LitStream

Chapter 3External Source

Brézin, Edouard; Hikami, Shinobu

Pages: 17 –23

[An external, i.e. deterministic, source matrix A is now coupled to the random matrices with weight \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 4Characteristic Polynomials and Duality

Brézin, Edouard; Hikami, Shinobu

Pages: 25 –35

[TheCharacteristic polynomials consideration of expectation values of characteristic polynomials was introduced in [85] (Keating, and Snaith, Commun. Math. Phys. 214, 57–89, 2000) for the unitary group. We here consider the Hermitian matrix for characteristic polynomials [24] (Brézin and Hikami,...
LitStream

Chapter 5Universality

Brézin, Edouard; Hikami, Shinobu

Pages: 37 –60

[The sine kernel was derived for the Gaussian unitary ensemble (GUE) by Dyson [50].]
LitStream

Chapter 6Intersection Numbers of Curves

Brézin, Edouard; Hikami, Shinobu

Pages: 61 –64

[Witten (Two dimensional gravity and intersection theory on moduli space, surveys in differential geometry 1, 243–310, 1991, [134]) conjectured that a generating function of the intersection numbers of the moduli space of curves on a Riemann surface with marked points, is a solution of the KdV...
LitStream

Chapter 7Intersection Numbers of p-Spin Curves

Brézin, Edouard; Hikami, Shinobu

Pages: 65 –98

[The duality formula presented in Chap. 4 and the explicit results for the n-point functions with an external source, make it possible to compute the intersection numbers of a moduli space of p-spin curves, a generalization of KontsevichIntersection number intersection numbers considered in the...
LitStream

Chapter 8Open Intersection Numbers

Brézin, Edouard; Hikami, Shinobu

Pages: 99 –111

[The intersection numbers are defined on the moduli space of Riemann surface with s-marked points and genus g. When Riemann surface is cut and has boundary, the open intersection numbers appear. There appear open strings which touch to the boundary.]
LitStream

Chapter 9Non-orientable Surfaces from Lie Algebras

Brézin, Edouard; Hikami, Shinobu

Pages: 113 –121

[Usually Feyman diagrams related to real symmetric matrices are used for generating non-orientable surfaces. The Euler characteristics of non-orientable surfaces have been derived from real symmetric matrices (Goulden et al., Trans Amer Math Soc 353:4405–4427, 2001, [68]). There are also studies...
LitStream

Chapter 10Gromov–Witten Invariants, P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{1}$$\end{document} Model

Brézin, Edouard; Hikami, Shinobu

Pages: 123 –129

[The intersection numbers of p-spin curves is a simple example of more generalGromov–Witten invariants Gromov–Witten invariants, where the manifold X is a point.]

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