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arXiv · 1812.01964

Large gap asymptotics for Airy kernel determinants with discontinuities

Christophe Charlier·Tom Claeys
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Abstract

We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number $m$ of discontinuities. These $m$-point determinants are generating functions for the Airy point process and encode probabilistic information about eigenvalues near soft edges in random matrix ensembles. Our main result is that the $m$-point determinants can be expressed asymptotically as the product of $m$ $1$-point determinants, multiplied by an explicit constant pre-factor which can be interpreted in terms of the covariance of the counting function of the process.

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Christophe Charlier, Tom Claeys. 2018-12-05. Large gap asymptotics for Airy kernel determinants with discontinuities. https://doi.org/10.1007/s00220-019-03538-w

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