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Janossy Densities I. Determinantal Ensembles

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arxiv math-ph/0212063 v4 pith:AU5ZUA6J submitted 2002-12-20 math-ph math.MPmath.PR

Alexei Borodin , Alexander Soshnikov This is my paper · ORCID
classification math-phmath.MPmath.PR
keywords densitiesjanossydeterminantalensembleskernelbetachristoffel-darbouxcomplement
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We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for beta=2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of I.

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  1. Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlev\'e VI distribution

    math-ph 2026-03 conditional novelty 7.0 of 10

    The full persistence distribution in 1D Ising coarsening equals a Pfaffian Fredholm determinant of the sech kernel and is controlled by a Painlevé VI equation that is the mean curvature of a Bonnet surface.

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