Rate of convergence in the central limit theorem for the determinantal point process with Bessel kernel

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We consider a family of linear operators diagonalized by the Hankel transform. We express explicitly the Fredholm determinants of these operators, as restricted to $L_2[0, R]$, so that the rate of their convergence as $R\to\infty$ can be found. We use the link between these determinants and the distribution of additive functionals in a determinantal point process with Bessel kernel and estimate the distance in the Kolmogorov–Smirnov metric between the distribution of these functionals and the Gaussian distribution. Bibliography: 27 titles.

Sobre autores

Sergei Gorbunov

Landau Phystech School of Physics and Research, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia; Ivannikov Institute for System Programming of the Russian Academy of Science, Moscow, Russia; Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Email: gorbunov.sm@phystech.edu

Bibliografia

  1. Zhigang Bao, Yukun He, Quantitative CLT for linear eigenvalue statistics of Wigner matricess
  2. E. L. Basor, Yang Chen, “A note on Wiener–Hopf determinants and the Borodin–Okounkov identity”, Integral Equations Operator Theory, 45:3 (2003), 301–308
  3. E. L. Basor, T. Ehrhardt, “Asymptotics of determinants of Bessel operators”, Comm. Math. Phys., 234:3 (2003), 491–516
  4. E. L. Basor, T. Ehrhardt, Determinant computations for some classes of Toeplitz–Hankel matrices
  5. E. L. Basor, T. Ehrhardt, H. Widom, On the determinant of a certain Wiener–Hopf + Hankel operator
  6. E. L. Basor, H. Widom, “On a Toeplitz determinant identity of Borodin and Okounkov”, Integral Equations Operator Theory, 37:4 (2000), 397–401
  7. S. Berezin, A. I. Bufetov, “On the rate of convergence in the central limit theorem for linear statistics of Gaussian, Laguerre, and Jacobi ensembles”, Pure Appl. Funct. Anal., 6:1 (2021), 57–99
  8. D. Betea, Correlations for symplectic and orthogonal Schur measures
  9. A. Böttcher, “On the determinant formulas by Borodin, Okounkov, Baik, Deift, and Rains”, Toeplitz matrices and singular integral equations, Oper. Theory Adv. Appl., 135, Birkhäuser Verlag, Basel, 2002, 91–99
  10. A. Böttcher, B. Silbermann, Analysis of Toeplitz operators, Springer Monogr. Math., 2nd ed., Springer-Verlag, Berlin, 2006, xiv+665 pp.
  11. A. Borodin, A. Okounkov, “A Fredholm determinant formula for Toeplitz determinants”, Integral Equations Operator Theory, 37:4 (2000), 386–396
  12. А. И. Буфетов, “Среднее значение мультипликативного функционала синус-процесса”, Функц. анализ и его прил., 58:2 (2024), 23–33
  13. A. I. Bufetov, The sine-process has excess one
  14. P. Deift, X. Zhou, “A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation”, Ann. of Math. (2), 137:2 (1993), 295–368
  15. T. Ehrhardt, “A generalization of Pincus' formula and Toeplitz operator determinants”, Arch. Math. (Basel), 80:3 (2003), 302–309
  16. В. Феллер, Введение в теорию вероятностей и ее приложения, т. 2, Мир, М., 1967, 752 с.
  17. И. С. Градштейн, И. М. Рыжик, Таблицы интегралов, сумм, рядов и произведений, 4-е изд., Физматгиз, М., 1963, 1100 с.
  18. K. Johansson, “On random matrices from the compact classical groups”, Ann. of Math. (2), 145:3 (1997), 519–545
  19. J. P. Keating, F. Mezzadri, B. Singphu, “Rate of convergence of linear functions on the unitary group”, J. Phys. A, 44:3 (2011), 035204, 27 pp.
  20. G. Lambert, M. Ledoux, C. Webb, “Quantitative normal approximation of linear statistics of $beta$-ensembles”, Ann. Probab., 47:5 (2019), 2619–2685
  21. O. Macchi, “The coincidence approach to stochastic point processes”, Adv. in Appl. Probab., 7 (1975), 83–122
  22. B. Simon, Operator theory, Compr. Course Anal., 4, Amer. Math. Soc., Providence, RI, 2015, xviii+749 pp.
  23. B. Simon, Orthogonal polynomials on the unit circle, Part 1. Classical theory, Amer. Math. Soc. Colloq. Publ., 54, Part 1, Amer. Math. Soc., Providence, RI, 2005, xxvi+466 pp.
  24. B. Simon, Trace ideals and their applications, Math. Surveys Monogr., 120, 2nd ed., Amer. Math. Soc., Providence, RI, 2005, viii+150 pp.
  25. А. Б. Сошников, “Детерминантные случайные точечные поля”, УМН, 55:5(335) (2000), 107–160
  26. C. A. Tracy, H. Widom, “Level spacing distributions and the Bessel kernel”, Comm. Math. Phys., 161:2 (1994), 289–309
  27. H. Widom, “A trace formula for Wiener–Hopf operators”, J. Operator Theory, 8:2 (1982), 279–298

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