On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices
Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 3, pp. 567-604.
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We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the matrix-size tends to infinity in terms of the volumes of certain regions involving continuous Gelfand–Tsetlin patterns with constraints. The results we find differ from those in the unitary case considered previously.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/127
Classification : 05-XX, 60-XX
Mots-clés : Moments of characteristic polynomials, Symplectic and orthogonal Gelfand-Tsetlin patterns, Symplectic and orthogonal Schur polynomials 
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     author = {Assiotis, Theodoros and Bailey, Emma and Keating, Jonathan},
     title = {On the moments of the moments of the characteristic polynomials of {Haar} distributed symplectic and orthogonal matrices},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {567--604},
     volume = {9},
     number = {3},
     year = {2022},
     doi = {10.4171/aihpd/127},
     mrnumber = {4526320},
     zbl = {1515.15032},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/127/}
}
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Assiotis, Theodoros; Bailey, Emma; Keating, Jonathan. On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices. Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 3, pp. 567-604. doi : 10.4171/aihpd/127. http://archive.numdam.org/articles/10.4171/aihpd/127/

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