Janossy densities, multimatrix spacing distributions and Fredholm resolvents
Mathematical Physics
2009-01-22 v3 Statistical Mechanics
High Energy Physics - Theory
math.MP
Probability
Exactly Solvable and Integrable Systems
Abstract
A simple proof is given for a generalized form of a theorem of Soshnikov. The latter states that the Janossy densities for multilevel determinantal ensembles supported on measurable subspaces of a set of measure spaces are constructed by dualization of bases on dual pairs of N-dimensional function spaces with respect to a pairing given by integration on the complements of the given measurable subspaces. The generalization extends this to dualization with respect to measures modified by arbitrary sets of weight functions.
Cite
@article{arxiv.math-ph/0403007,
title = {Janossy densities, multimatrix spacing distributions and Fredholm resolvents},
author = {J. Harnad},
journal= {arXiv preprint arXiv:math-ph/0403007},
year = {2009}
}
Comments
PlainTex, 10 pages. Some notational corrections added. References updated. To appear in: International Mathematics Research notices