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Homepage of Tom Claeys - Research


  • Papers

    • M. Cafasso and T. Claeys, Biorthogonal measures, polymer partition functions, and random matrices (arxiv:2401.10130).
    • T. Claeys, G. Glesner, G. Ruzza, and S. Tarricone, Janossy densities and Darboux transformations for the Stark and cylindrical KdV equations (arxiv:2303.09848).
    • T. Claeys and S. Tarricone, On the integrable structure of deformed sine kernel determinants, to appear in Mathematical Physics, Analysis and Geometry (arxiv:2309.03803).
    • T. Claeys, I. Krasovsky, and O. Minakov, Weak and strong confinement in the Freud random matrix ensemble and gap probabilities, Commun. Math. Phys. 402, 833–894 (2023), (arxiv:2209.07253).
    • T. Claeys and G. Glesner, Determinantal point processes conditioned on randomly incomplete configurations, Ann. Inst. H. Poincare. Prob. Stat.59 (2023), no. 4, 2189–2219 (arxiv:2112.10642).
    • T. Claeys, J. Forkel, and J. Keating, Moments of Moments of the Characteristic Polynomials of Random Orthogonal and Symplectic Matrices, Proc. R. Soc. A 479:20220652 (2022) http://doi.org/10.1098/rspa.2022.0652 (arxiv:2209.06010).
    • T. Claeys and D. Wang, Universality for random matrices with equi-spaced external source: a case study of a biorthogonal ensemble, J. Stat. Phys. 188, Article number: 11 (2022) (arxiv:2202.03827).
    • C. Charlier, T. Claeys, and G. Ruzza, Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ, Journal of Functional Analysis 283, no. 8, article 109608 (2022) (arxiv:2111.14569).
    • M. Cafasso and T. Claeys, A Riemann-Hilbert approach to the lower tail of the KPZ equation, Comm. Pure Appl. Math. 75 (2022), no. 3, 493–540 (arxiv:1910.02493).
    • M. Cafasso, T. Claeys, and G. Ruzza, Airy kernel determinant solutions of the KdV equation and integro-differential Painlevé equations, Comm. Math. Phys. 386 (2021), no. 2, 1107–1153 (arxiv:2008.07785).
    • T. Claeys, G. Glesner, A. Minakov, and M. Yang, Asymptotics for averages over classical orthogonal ensembles, Int. Math. Res. Notices (2021), rnaa354, https://doi.org/10.1093/imrn/rnaa354 (arxiv:2008.07785).
    • C. Charlier and T. Claeys, Global rigidity and exponential moments for soft and hard edge point processes, Prob. Math. Phys. 2 (2021), no. 2, 363–417, doi: 10.2140/pmp.2021.2.363 (arxiv:2002.03833).
    • T. Claeys, B. Fahs, G. Lambert, and C. Webb, How much can the eigenvalues of a random Hermitian matrix fluctuate?, Duke Math. J. 170 (2021), no. 9, 2085–2235 (arxiv:1906.01561).
    • T. Claeys, T. Neuschel, and M. Venker, Critical Behavior of Non-Intersecting Brownian Motions, Comm. Math. Phys. (2020), https://doi.org/10.1007/s00220-020-03823-z (arxiv:1912.02142).
    • C. Charlier and T. Claeys, Large gap asymptotics for Airy kernel determinants with discontinuities, Comm. Math. Phys. (2019), https://doi.org/10.1007/s00220-019-03538-w (arxiv:1812.01964).
    • M. Cafasso, T. Claeys, and M. Girotti, Fredholm determinant solutions of the Painlevé II hierarchy and gap probabilities of determinantal point processes, Int. Math. Res. Notices (2019), rnz168, https://doi.org/10.1093/imrn/rnz168 (arxiv:1812.01964).
    • T. Claeys, T. Neuschel, and M. Venker, Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices, Random Matrices: Theory and Appl. 8 (2019), no. 3, 1950011, 50 pp (arxiv:1712.08432).
    • T. Claeys, A. Kuijlaars, K. Liechty, and D. Wang, Propagation of singular behavior for Gaussian perturbations of random matrices, Comm. Math. Phys. 362 (2018), no. 1, 1–54 (arxiv:1608.05870).
    • T. Claeys and A. Doeraene, The generating function for the Airy point process and a system of coupled Painlevé II equations, Stud. Appl. Math. 140 (2018), no. 4, 403–437 (arxiv:1708.03481).
    • T. Claeys, M. Girotti, and D. Stivigny, Large gap asymptotics at the hard edge for product random matrices and Muttalib-Borodin ensembles, Int. Math. Res. Notices 2017 (2017), doi: 10.1093/imrn/rnx202, 48 pages (arxiv:1612.01916).
    • C. Charlier and T. Claeys, Thinning and conditioning of the Circular Unitary Ensemble, Random Matrices: Theory and Applications 6 (2017), no. 2, 1750007 (arxiv:1604.08399).
    • A. Bogatskiy, T. Claeys, and A. Its, Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge, Comm. Math. Phys. 347 (2016), no. 1, 127–162 (arxiv:1507.01710).
    • T. Claeys and A. Doeraene, Gaussian perturbations of hard edge random matrix ensembles, Nonlinearity 29 (2016), no. 11, 3385 (arxiv:1601.00511).
    • T. Claeys and B. Fahs, Random matrices with merging singularities and the Painlevé V equation, SIGMA 12 (2016), 031, 44 pages, Special Issue on Asymptotics and Universality in Random Matrices, Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy (arxiv:1508.06734).
    • T. Claeys and I. Krasovsky, Toeplitz determinants with merging singularities, Duke Math. J. 164 (2015), no. 15, 2897-2987 (arxiv:1403.3639).
    • T. Claeys, A. Kuijlaars, and D. Wang, Correlation kernels for sums and products of random matrices, Random Matrices: Theory and Applications 4, no. 4 (2015), 1550017 (arxiv:1505.00610).
    • M. Atkin, T. Claeys, and F. Mezzadri, Random matrix ensembles with singularities and a hierarchy of Painlevé III equations, Int. Math. Res. Notices 2015 (2015), doi: 10.1093/imrn/rnv195, 56 pages (arxiv:1501.04475).
    • T. Claeys, T. Grava, and K. T-R McLaughlin, Asymptotics for the partition function in two-cut random matrix models, Comm. Math. Phys. 339, no. 2 (2015), 513-587 (arxiv:1410.7001).
    • C. Charlier and T. Claeys, Asymptotics for Toeplitz determinants: perturbation of symbols with a gap, J. Math. Phys 56 (2015), 022705 (arxiv:1409.0435).
    • T. Claeys and S. Romano, Biorthogonal ensembles with two-particle interactions, Nonlinearity 27 (2014), 2419-2443 (arxiv:1312.2892).
    • T. Claeys and D. Wang, Random matrices with equispaced external source, Comm. Math. Phys. 328, no. 3 (2014), 1023-1077 (arxiv:1212.3768).
    • T. Claeys and T. Grava, Critical asymptotic behavior for the Korteweg-de Vries equation and in random matrix theory, Random Matrices, MSRI Publications, Volume 65, Cambridge University Press (2014) (arxiv:1210.8352).
    • T. Claeys and F. Wielonsky, On sequences of rational interpolants of the exponential function with unbounded interpolation points, Journal of Approximation Theory 171 (2013), 1-32 (arxiv:1112.2887).
    • T. Claeys and S. Olver, Numerical study of higher order analogues of the Tracy-Widom distribution, in “Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications”, Contemporary Mathematics 578, Amer. Math. Soc., Providence R.I. 2012, 83-99 (arxiv:1111.3527).
    • T. Claeys, Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation, Physica D 241 (2012) 2226–2236 (arxiv:1107.0214).
    • T. Claeys, The Riemann-Hilbert approach to obtain critical asymptotics for Hamiltonian perturbations of hyperbolic and elliptic systems, Random Matrices: Theory and Applications 1 (2012) 1130002 (arxiv:1111.3531).
    • T. Claeys and T. Grava, The KdV hierarchy: universality and a Painlevé transcendent, Int. Math. Res. Notices 2011; doi: 10.1093/imrn/rnr220, 37 pages (arxiv:1101.2602).
    • T. Claeys, A. Its, and I. Krasovsky, Emergence of a singularity for Toeplitz determinants and Painlevé V, Duke Math. Journal 160, no. 2 (2011), 207-262 (arxiv:1004.3696).
    • T. Claeys and T. Grava, Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit, SIAM Journal on Mathematical Analysis 42, no. 5 (2010), 2132-2154 (arxiv:0911.5686).
    • T. Claeys, Asymptotics for a special solution to the second member of the Painlevé I hierarchy, J. Phys. A: Math. Theor. 43 (2010) 434012 (18pp) (arxiv:1001.2213).
    • T. Claeys, A. Its, and I. Krasovsky, Higher order analogues of the Tracy-Widom distribution and the Painlevé II hierarchy, Comm. Pure Appl. Math. 63 (2010), 362-412 (arxiv:0901.2473).
    • T. Claeys and T. Grava, Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit, Comm. Pure Appl. Math. 63 (2010), 203-232 (arxiv:0812.4142).
    • T. Claeys and T. Grava, Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach, Comm. Math. Phys. 286 (2009), 979-1009 (arxiv:0801.2326).
    • T. Claeys, A. Kuijlaars, and M. Vanlessen, Multi-critical unitary random matrix ensembles and the general Painlevé II equation, Ann. Math. 167 (2008), 601-642 (math-ph/0508062).
    • T. Claeys, The birth of a cut in unitary random matrix ensembles, Int. Math. Res. Notices (2008) Vol. 2008, doi:10.1093/imrn/rnm166, 40 pages (arxiv:0711.2609).
    • T. Claeys and A. Kuijlaars, Universality in unitary random matrix ensembles when the soft edge meets the hard edge, in "Integrable Systems and Random Matrices: in honor of Percy Deift", Contemporary Mathematics 458, Amer. Math. Soc., Providence R.I. 2008, 265-280 (math-ph/0701003).
    • T. Claeys and M. Vanlessen, Universality of a double scaling limit near singular edge points in random matrix models, Comm. Math. Phys. 273 (2007), 499-532 (math-ph/0607043).
    • T. Claeys and M. Vanlessen, The existence of a real pole-free solution of the fourth order analogue of the Painlevé I equation, Nonlinearity 20 (2007), 1163-1184 (math-ph/0604046).
    • T. Claeys and A. Kuijlaars, Universality of the double scaling limit in random matrix models, Comm. Pure Appl. Math. 59, no. 11 (2006), 1573-1603 (math-ph/0501074).


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