Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices

Abstract

We present new and streamlined proofs of various formulae for products and ratios of characteristic polynomials of random Hermitian matrices that have appeared recently in the literature.

18 pages, LaTex

References in corpus (1)

• An exact formula for general spectral correlation function of random Hermitian matrices

Cited by in corpus (60)

• On the averages of characteristic polynomials from classical groups
• Painleve IV and degenerate Gaussian Unitary Ensembles
• Derivation of determinantal structures for random matrix ensembles in a new way
• Relating the Bures measure to the Cauchy two-matrix model
• Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N)
• Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry
• FZZT branes in JT gravity and topological gravity
• On the distribution of maximum value of the characteristic polynomial of GUE random matrices
• On absolute moments of characteristic polynomials of a certain class of complex random matrices
• Products of Independent Gaussian Random Matrices
• $\mathcal{N}=2$ conformal gauge theories at large R-charge: the $SU(N)$ case
• Ratios of characteristic polynomials in complex matrix models
• On matrix model partition functions for QCD with chemical potential
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
• Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels
• On characteristic polynomials for a generalized chiral random matrix ensemble with a source
• On the asymptotics of some large Hankel determinants generated by Fisher-Hartwig symbols defined on the real line
• Correlations of RMT Characteristic Polynomials and Integrability: Hermitean Matrices
• On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix
• Asymptotics for products of characteristic polynomials in classical $\beta$-Ensembles
• Exact equivalences and phase discrepancies between random matrix ensembles
• Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
• Painleve formulas of the limiting distributions for non-null complex sample covariance matrices
• Fermionic approach to the evaluation of integrals of rational symmetric functions
• Autocorrelation of ratios of L-functions
• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• Average characteristic polynomials in the two-matrix model
• Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices
• Zooming in on local level statistics by supersymmetric extension of free probability
• Correlation Functions of Complex Matrix Models
• Averages of products and ratios of characteristic polynomials in polynomial ensembles
• On the moments of characteristic polynomials
• Integrals of rational symmetric functions, two matrix models and biorthogonal polynomials
• On the second mixed moment of the characteristic polynomials of the 1D band matrices
• Characteristic polynomials for random band matrices near the threshold
• Exact cubature rules for symmetric functions
• Superposition of Random Plane Waves in High Spatial Dimensions: Random Matrix Approach to Landscape Complexity
• Autocorrelations of the characteristic polynomial of a random matrix under microscopic scaling
• Matrix models for stationary Gromov-Witten invariants of the Riemann sphere
• Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles
• Survival Probability of a Doorway State in regular and chaotic environments
• Cubature rules for unitary Jacobi ensembles
• Asymptotics of Characteristic Polynomials of Wigner Matrices at the Edge of the Spectrum
• On permanental polynomials of certain random matrices
• On the correlation functions of the characteristic polynomials of the hermitian sample covariance ensemble
• Radial Toeplitz operators and invariant determinantal point processes on Cayley trees
• Symmetric Function Theory and Unitary Invariant Ensembles
• Giambelli compatible point processes
• Total-positivity preservers
• Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality
• Strong asymptotics of Laguerre-type orthogonal polynomials and applications in random matrix theory
• Limits for circular Jacobi beta-ensembles
• A universality theorem for ratios of random characteristic polynomials
• On the Second-Order Correlation Function of the Characteristic Polynomial of a Real Symmetric Wigner Matrix
• Phase transitions for products of characteristic polynomials under Dyson Brownian motion
• Average characteristic polynomials for multiple orthogonal polynomial ensembles
• Autocorrelations of characteristic polynomials for the Alternative Circular Unitary Ensemble
• Characteristic Polynomials of Sample Covariance Matrices
• The Schur Expansion of Characteristic Polynomials and Random Matrices