Average characteristic polynomials of determinantal point processes

DOI10.1214/13-AIHP572zbMath1332.60023arXiv1211.6564OpenAlexW3105774134MaRDI QIDQ2261599

Adrien Hardy

Publication date: 9 March 2015

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.6564

zbMATH Keywords

strong law of large numbersrandom matricesmultiple orthogonal polynomialsdeterminantal point processesaverage characteristic polynomials

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Strong limit theorems (60F15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Convergence of probability measures (60B10) Real polynomials: location of zeros (26C10)

Related Items (16)

Asymptotics for characteristic polynomials of Wishart type products of complex Gaussian and truncated unitary random matrices ⋮ Wigner matrices, the moments of roots of Hermite polynomials and the semicircle law ⋮ On inherited properties and Julia sets of exceptional Jacobi polynomials ⋮ Multiplication operator and average characteristic polynomial associated with exceptional Jacobi polynomials ⋮ Monte Carlo with determinantal point processes ⋮ Polynomial ensembles and recurrence coefficients ⋮ On a few statistical applications of determinantal point processes ⋮ Volumes for \(\text{SL}_N(\mathbb{R})\), the Selberg integral and random lattices ⋮ Limit theorems for biorthogonal ensembles and related combinatorial identities ⋮ A note on the limiting mean distribution of singular values for products of two Wishart random matrices ⋮ Spectral curves, variational problems and the Hermitian matrix model with external source ⋮ Statistical behavior of the characteristic polynomials of a family of pseudo-Hermitian Gaussian matrices ⋮ Asymptotics for recurrence coefficients of X₁-Jacobi exceptional polynomials and Christoffel function ⋮ Global fluctuations for multiple orthogonal polynomial ensembles ⋮ Christoffel functions for multiple orthogonal polynomials ⋮ Raney distributions and random matrix theory

Uses Software

• RMTool

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