Janossy Densities of Coupled Random Matrices

Abstract

We explicitly calculate Janossy densities for a special class of finite determinantal point processes with several types of particles introduced by Prähofer and Spohn and, in the full generality, by Johansson in connection with the analysis of polynuclear growth models. The results of our paper generalize the theorem we proved earlier with Borodin about the Janossy densities in biorthogonal ensembles. In particular, our results can be applied to coupled random matrices.

We revised the introduction and added a couple of new references

References in corpus (9)

• Discrete polynuclear growth and determinantal processes
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Scale Invariance of the PNG Droplet and the Airy Process
• Dynamical Correlations among Vicious Random Walkers
• Step fluctuations for a faceted crystal
• Janossy Densities I. Determinantal Ensembles
• Janossy Densities II. Pfaffian Ensembles
• Stochastic Growth in One Dimension and Gaussian Multi-Matrix Models
• Janossy densities, multimatrix spacing distributions and Fredholm resolvents

Cited by in corpus (8)

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• Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals
• Noncolliding processes, matrix-valued processes and determinantal processes
• Statistics of Extreme Spacings in Determinantal Random Point Processes
• Tracy-Widom distributions for the Gaussian orthogonal and symplectic ensembles revisited: a skew-orthogonal polynomials approach
• Janossy densities, multimatrix spacing distributions and Fredholm resolvents
• Determinantal identity for multilevel systems and finite determinantal processes