The expectation of a multiplicative functional under the sine-process
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 23-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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An explicit expression for the expected value of a regularized multiplicative functional under the sine-process is obtained by passing to the scaling limit in the Borodin–Okounkov–Geronimo–Case formula.
Keywords: sine-process, multiplicative functional, Wiener–Hopf operator
Mots-clés : Borodin–Okounkov–Geronimo–Case formula.
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Alexander Bufetov. The expectation of a multiplicative functional under the sine-process. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 23-33. http://geodesic.mathdoc.fr/item/FAA_2024_58_2_a2/

[1] C. Andréief, “Note sur une relation entre les intégrales définies des produits des fonctions”, Mém. Soc. Sci. Phys. Nat. Bordeaux, 2 (1886), 1–14 | Zbl

[2] E. Basor, Yang Chen, A note on Wiener–Hopf determinants and the Borodin–Okounkov identity, arXiv: math/0202062

[3] E. L. Basor, H. Widom, “On a Toeplitz determinant identity of Borodin and Okounkov”, Integral Equations Operator Theory, 37:4 (2000), 397–401 | DOI | MR | Zbl

[4] A. Borodin, A. Okounkov, “A Fredholm determinant formula for Toeplitz determinants”, Integral Equations Operator Theory, 37:4 (2000), 386–396 | DOI | MR | Zbl

[5] A. Böttcher, On the determinant formulas by Borodin, Okounkov, Baik, Deift, and Rains, arXiv: math/0101008

[6] A. Böttcher, “One more proof of the Borodin–Okounkov formula for Toeplitz determinants”, Integral Equations Operator Theory, 41:1 (2001), 123–125 | DOI | MR | Zbl

[7] A. I. Bufetov, “Quasi-symmetries of determinantal point processes”, Ann. Probab., 46:2 (2018), 956–1003 | DOI | MR | Zbl

[8] A. I. Bufetov, The sine-process has excess one, arXiv: 1912.13454

[9] P. Deift, A. Its, I. Krasovsky, “Toeplitz matrices and Toeplitz determinants under the impetus of the Ising model: some history and some recent results”, Comm. Pure Appl. Math., 66:9 (2013), 1360–1438 | DOI | MR | Zbl

[10] J. S. Geronimo, K. M. Case, “Scattering theory and polynomials orthogonal on the unit circle”, J. Math. Phys., 20:2 (1979), 299–310 | DOI | MR | Zbl

[11] B. L. Golinskiĭ, I. A. Ibragimov, “On Szegö's limit theorem”, Math. USSR-Izv., 5:2 (1971), 421–444 | DOI | MR | Zbl

[12] U. Grenander, G. Szegö, Toeplitz forms and their applications, California Monogr. Math. Sci., Univ. of California Press, Berkeley–Los Angeles, 1958, vii+245 pp. | MR | MR | Zbl | Zbl

[13] I. A. Ibragimov, “On a theorem of G. Szegö”, Math. Notes, 3:6 (1968), 442–448 | DOI | MR | Zbl

[14] B. Simon, Orthogonal polynomials on the unit circle, Parts 1, 2, Amer. Math. Soc. Colloq. Publ., 54, Amer. Math. Soc., Providence, RI, 2005, xxvi+466 pp., i–xxii and 467–1044 pp. | MR | MR | Zbl

[15] G. Szegö, “Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reellen positiven Funktion”, Math. Ann., 76:4 (1915), 490–503 | DOI | MR | Zbl

[16] G. Szegö, “On certain Hermitian forms associated with the Fourier series of a positive function”, Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.], 1952, Tome Suppl. – Festschrift M. Riesz (1952), 228–238 | MR | Zbl