Lectures on Random Matrix Models (Q2908886)

scientific article; zbMATH DE number 6073562

Language	Label	Description	Also known as
English	Lectures on Random Matrix Models	scientific article; zbMATH DE number 6073562

Statements

instance of

scholarly article

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title

Lectures on Random Matrix Models (English)

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published in

Random Matrices, Random Processes and Integrable Systems

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publication date

29 August 2012

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full work available at URL

https://arxiv.org/abs/0801.1858

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zbMATH Keywords

Riemann-Hilbert approach

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random matrix models

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asymptotics

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partition function

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external source

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orthogonal polynomials

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Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum.

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PDEs for the joint distributions of the Dyson, Airy and Sine processes

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Multiple orthogonal polynomials

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Large \(n\) limit of Gaussian random matrices with external source. II

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Multiple orthogonal polynomials for classical weights

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On the distribution of the length of the longest increasing subsequence of random permutations

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Q3994426

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Partition functions for matrix models and isomonodromic tau functions

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Differential systems for biorthogonal polynomials appearing in 2-Matrix models and the associated Riemann-Hilbert problem

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Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions

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Quantum field theory techniques in graphical enumeration

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Double scaling limit in random matrix models and a nonlinear hierarchy of differential equations

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Exact solution of the six-vertex model with domain wall boundary conditions. Disordered phase

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Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model

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Double scaling limit in the random matrix model: The Riemann-Hilbert approach

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Asymptotics of the partition function of a random matrix model.

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Q5693356

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Large \(n\) limit of Gaussian random matrices with external source. I

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Integral representations for multiple Hermite and multiple Laguerre polynomials.

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Large \(n\) limit of Gaussian random matrices with external source. III: Double scaling limit

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Breakdown of universality in multi-cut matrix models

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On the statistical mechanics approach in the random matrix theory: Integrated density of states.

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Correlations of nearby levels induced by a random potential

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Planar diagrams

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Universality of the correlations between eigenvalues of large random matrices.

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Symmetry breaking in the double-well Hermitian matrix models

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Eigenvalue correlations on hyperelliptic Riemann surfaces

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Ladder operators and differential equations for orthogonal polynomials

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Thermodynamic relations of the Hermitian matrix ensembles

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Universality of the double scaling limit in random matrix models

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Factorization of matrix functions and singular integral operators

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Square ice, alternating sign matrices, and classical orthogonal polynomials

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LOOP EQUATIONS AND THE TOPOLOGICAL PHASE OF MULTI-CUT MATRIX MODELS

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A Christoffel--Darboux formula for multiple orthogonal polynomials

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New results on the equilibrium measure for logarithmic potentials in the presence of an external field

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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory

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Q4487945

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A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation

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Matrix model combinatorics: applications to folding and coloring.

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Q3935915

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Painlevé I asymptotics for orthogonal polynomials with respect to a varying quartic weight

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Correlations between eigenvalues of a random matrix

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Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices

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Q4800290

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Q4002564

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The isomonodromy approach to matrix models in 2D quantum gravity

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The spectrum edge of random matrix ensembles.

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Nonperturbative two-dimensional quantum gravity

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The isomonodromic deformation method in the theory of Painlevé equations

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The planar approximation. II

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On fluctuations of eigenvalues of random Hermitian matrices.

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Turning points of linear systems and the double asymptotics of the Painlevé transcendents

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Q4254650

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Q4432379

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Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields

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A Riemann-Hilbert problem for biorthogonal polynomials

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Factorization of measurable matrix functions. Ed. by Georg Heinig. Transl. from the Russian by Bernd Luderer. With a foreword by Bernd Silbermann. (Licensed ed.)

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Q4001740

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Geometry of the string equations

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Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles

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Q4360405

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Universality in orthogonal and symplectic invariant matrix models with quartic potential

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Q4284356

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Level-spacing distributions and the Airy kernel

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The Pearcey process

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Riemann-Hilbert problems for multiple orthogonal polynomials

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Q4012873

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The Riemann–Hilbert Problem and Inverse Scattering

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Random Hermitian matrices in an external field

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Universality of correlation functions of Hermitian random matrices in an external field

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reviewed by

Ludwig Kohaupt

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Identifiers

zbMATH Open document ID

1252.15040

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DOI

10.1007/978-1-4419-9514-8_4

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:2908886