Large gap asymptotics for Airy kernel determinants with discontinuities

Charlier, Christophe;Claeys, Tom
(2020) Communications in Mathematical Physics — Vol. 375, n° 2, p. 1299-1339 (2020)

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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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Charlier, C., & Claeys, T. (2020). Large gap asymptotics for Airy kernel determinants with discontinuities. Communications in Mathematical Physics, 375(2), 1299-1339. https://doi.org/10.1007/s00220-019-03538-w (Original work published 2020)