On the Moments of the Partition Function of the C$$\beta $$E Field-Reference-Cited by-同舟云学术

On the Moments of the Partition Function of the C$$\beta $$E Field

Published:2022-03-18 Issue:2 Volume:187 Page:
ISSN:0022-4715
Container-title:Journal of Statistical Physics
language:en
Short-container-title:J Stat Phys

Author:

Assiotis Theodoros^ORCID

Abstract

AbstractWe obtain a combinatorial formula for the positive integer moments of the partition function of the

$$C\beta E_{N}$$

C β E N field, or equivalently the moments of the moments of the characteristic polynomial of the

$$C\beta E_{N}$$

C β E N ensemble. We then use this formula to establish the large N asymptotics of these moments in the “moment-supercritical” regime. A key role is played by Jack polynomials.

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://link.springer.com/content/pdf/10.1007/s10955-022-02906-6.pdf

Reference43 articles.

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2. Assiotis, T., Bailey, E.C., Keating, J.P.: On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices, to appear Annales de l’Institut Henri Poincare D, arXiv:1910.12576, (2019)

3. Assiotis, T., Keating, J.P.: Moments of moments of characteristic polynomials of random unitary matrices and lattice point counts, to appear at RMTA, https://doi.org/10.1142/S2010326321500192, arXiv:1905.06072

4. Assiotis, T., Najnudel, J.: The boundary of the orbital beta process, to appear Moscow Math. J., arXiv:1905.08684, (2019)

5. Bailey, E.C., Keating, J.P.: On the moments of the moments of the characteristic polynomials of random unitary matrices. Commun. Math. Phys. 371, 689–726 (2019)

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