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  • 1.
    Charlier, Christophe
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Claeys, Tom
    Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Chemin du Cyclotron 2, Louvain-la-Neuve, 1348, Belgium.
    Large Gap Asymptotics for Airy Kernel Determinants with Discontinuities2019In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Charlier, Christophe
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lenells, Jonatan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Airy and Painleve asymptotics for the mKdV equation2019In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750Article in journal (Refereed)
    Abstract [en]

    We consider the higher order asymptotics for the modified Korteweg-de Vries equation in the Painleve sector. We first show that the solution admits a uniform expansion to all orders in powers of t-1/3 with coefficients that are smooth functions of x(3t)-1/3. We then consider the special case when the reflection coefficient vanishes at the origin. In this case, the leading coefficient which satisfies the Painleve II equation vanishes. We show that the leading asymptotics are instead described by the derivative of the Airy function. We are also able to express the subleading term explicitly in terms of the Airy function.

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