Spectral curves, variational problems and the Hermitian matrix model with external source (Q2021638)

scientific article; zbMATH DE number 7340022

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English	Spectral curves, variational problems and the Hermitian matrix model with external source	scientific article; zbMATH DE number 7340022

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instance of

scholarly article

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title

Spectral curves, variational problems and the Hermitian matrix model with external source (English)

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author

Guilherme L. F. Silva

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Andrei Martínez Finkelshtein

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published in

Communications in Mathematical Physics

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publication date

27 April 2021

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full work available at URL

https://arxiv.org/abs/1907.08108

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describes a project that uses

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Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half‐Plane

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Universality for general Wigner-type matrices

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A law of large numbers for finite-range dependent random matrices

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Hermite-Padé Approximants for a Pair of Cauchy Transforms with Overlapping Symmetric Supports

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

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On the limit behavior of recurrence coefficients for multiple orthogonal polynomials

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Systems of Markov functions generated by graphs and the asymptotics of their Hermite-Padé approximants

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Global eigenvalue distribution regime of random matrices with an anharmonic potential and an external source

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Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials

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Nuttall's Abelian integral on the Riemann surface of the cube root of a polynomial of degree 3

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Random Matrix Ensembles with Singularities and a Hierarchy of Painlevé III Equations

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Optimal tail estimates for directed last passage site percolation with geometric random variables

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On the Largest Eigenvalue of a Hermitian Random Matrix Model with Spiked External Source I. Rank 1 Case

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On the Largest Eigenvalue of a Hermitian Random Matrix Model with Spiked External Source II: Higher Rank Cases

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Boutroux curves with external field: equilibrium measures without a variational problem

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Universality conjecture and results for a model of several coupled positive-definite matrices

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Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes

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Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes

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Duality, biorthogonal polynomials and multi-matrix models

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

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Duality of spectral curves arising in two-matrix models

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Partition functions for matrix models and isomonodromic tau functions

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Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions

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Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights

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Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation

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Subharmonic Configurations and Algebraic Cauchy Transforms of Probability Measures

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Painlevé I double scaling limit in the cubic random matrix model

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Topological Expansion in the Cubic Random Matrix Model

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Random matrix model with external source and a constrained vector equilibrium problem

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

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

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Q5693356

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

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The Mother Body Phase Transition in the Normal Matrix Model

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On mother body measures with algebraic Cauchy transform

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Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions

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Corrigendum: ``Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions''

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Universality of mesoscopic fluctuations for orthogonal polynomial ensembles

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Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients

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Random Matrix Theory with an External Source

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Multi-critical unitary random matrix ensembles and the general Painlevé II equation

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Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices

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Asymptotics of Orthogonal Polynomials and the Painlevé Transcendents

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Painlevé kernels in Hermitian matrix models

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On Mesoscopic Equilibrium for Linear Statistics in Dyson’s Brownian Motion

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

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Universality for random matrix flows with time-dependent density

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A Dynamical Approach to Random Matrix Theory

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Interlacing properties of zeros of multiple orthogonal polynomials

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Average characteristic polynomials of determinantal point processes

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Q5703969

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On fluctuations of eigenvalues of random Hermitian matrices.

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Multiple orthogonal polynomial ensembles

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Multiple orthogonal polynomials in random matrix theory

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Asymptotic behavior of quadratic Hermite-Padé approximants to the exponential function and Riemann-Hilbert problems

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The supercritical regime in the normal matrix model with cubic potential

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Limit theorems for biorthogonal ensembles and related combinatorial identities

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Fixed energy universality of Dyson Brownian motion

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Convergence of local statistics of Dyson Brownian motion

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Q5493476

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Trajectories of quadratic differentials for Jacobi polynomials with complex parameters

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Riemann--Hilbert analysis for Jacobi polynomials orthogonal on a single contour

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Critical measures for vector energy: global structure of trajectories of quadratic differentials

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Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight

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Asymptotic analysis of random matrices with external source and a family of algebraic curves

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Q4001531

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Q4052427

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The asymptotics of Hermite-Padé polynomials for two Markov-type functions

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The polynomial method for random matrices

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Q4360405

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On spectral polynomials of the Heun equation. I

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Q3338499

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Nearest neighbor recurrence relations for multiple orthogonal polynomials

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Riemann-Hilbert problems for multiple orthogonal polynomials

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Large \(\mathrm{N}\)-limit for random matrices with external source with three distinct eigenvalues

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Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system

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Random Hermitian matrices in an external field

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Identifiers

Mathematics Subject Classification ID

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10.1007/S00220-021-03999-Y

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Sitelinks

Mathematics(1 entry)

mardi Publication:2021638