Аннотация:
We survey the current status of universality limits for $m$-point correlation functions in the bulk and at the edge for unitary ensembles, primarily when the limiting kernels are Airy, Bessel, or Sine kernels. In particular, we consider underlying measures on compact intervals, and fixed and varying exponential weights, as well as universality limits for a variety of orthogonal systems. The scope of the survey is quite narrow: we do not consider $\beta$ ensembles for $\beta \neq 2$, nor general Hermitian matrices with independent entries, let alone more general settings. We include some open problems.
Образец цитирования:
Doron S. Lubinsky, “An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles”, SIGMA, 12 (2016), 078, 36 pp.
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\paper An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles
\jour SIGMA
\yr 2016
\vol 12
\papernumber 078
\totalpages 36
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\crossref{https://doi.org/10.3842/SIGMA.2016.078}
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Эта публикация цитируется в следующих 13 статьяx:
Grzegorz Świderski, Bartosz Trojan, “Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case”, Annales de l'Institut Fourier, 74:4 (2024), 1521
Swiderski G., Trojan B., “Asymptotic Behaviour of Christoffel-Darboux Kernel Via Three-Term Recurrence Relation i”, Constr. Approx., 54:1 (2021), 49–116
Breuer J., “Scaling Limits of Jacobi Matrices and the Christoffel-Darboux Kernel”, Constr. Approx., 53:2 (2021), 349–379
Charlier Ch., “Large Gap Asymptotics For the Generating Function of the Sine Point Process”, Proc. London Math. Soc., 123:2 (2021), 103–152
G. Swiderski, B. Trojan, “Asymptotic behavior of Christoffel-Darboux kernel via three-term recurrence relation II”, J. Approx. Theory, 261 (2021), 105496
G. Swiderski, B. Trojan, “Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients”, J. Funct. Anal., 278:3 (2020), UNSP 108326
J. Breuer, E. Seelig, “On the spacing of zeros of paraorthogonal polynomials for singular measures”, J. Approx. Theory, 259 (2020), 105482
A. B. J. Kuijlaars, E. Mina-Diaz, “Universality for conditional measures of the sine point process”, J. Approx. Theory, 243 (2019), 1–24
T. Claeys, T. Neuschel, M. Venker, “Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices”, Random Matrices-Theor. Appl., 8:3 (2019), 1950011
G. Swiderski, “Periodic perturbations of unbounded Jacobi matrices III: the soft edge regime”, J. Approx. Theory, 233 (2018), 1–36
G. Swiderski, “Spectral properties of block Jacobi matrices”, Constr. Approx., 48:2 (2018), 301–335
E. Levin, D. Lubinsky, Bounds and asymptotics for orthogonal polynomials for varying weights, SpringerBriefs in Mathematics, Springer, 2018, 170 pp.
A. P. Horvath, K. S. Kazarian, “The Dirichlet problem in weighted norm”, Acta Math. Hung., 153:1 (2017), 34–56
Цитирование в формате AMSBIB
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