Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals

Gisonni, Massimo; Grava, Tamara; Ruzza, Giulio

doi:10.48550/arxiv.1912.00525

Cited by 4 publications

(6 citation statements)

References 45 publications

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“…Perhaps our polynomials P µ,d (α ′ ) and k ρ,d (α ′ ) may have some interpretation in terms of such enumeration. In fact, this connection has already been stablished for the α = 1 case in [40]. This topic deserves further study.…”

mentioning

confidence: 68%

Time delay statistics for finite number of channels in all symmetry classes

Novaes

2022

Preprint

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Within a random matrix theory approach, we obtain spectral statistics of the Wigner time delay matrix Q, for arbitrary channels number M and for all symmetry classes, in fact for general Dyson parameter β. For small values of M , the observables develop singularities at fractional values of β which may be of physical consequence in situations of partial breaking of the time-reversal symmetry. We also put forth two conjectures: one is related to the large-M expansion of joint cumulants of traces of powers of Q, which generalizes and implies a previous conjecture of Cunden, Mezzadri, Vivo and Simm; the other concerns the tail of the distribution of traces of powers of Q.

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confidence: 68%

Time delay statistics for finite number of channels in all symmetry classes

Novaes

2022

Preprint

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“…Recently the study of moments and joint moments of Hermitian ensembles have attracted considerable interest [10,11,13,24]. Here we give new and self contained formulae for the joint moments of unitary ensembles in terms of characters of the symmetric group.…”

Section: Joint Moments Of Tracesmentioning

confidence: 97%

“…Cunden, Dahlqvist and O'Connell [10] showed that the cumulants of the Laguerre ensemble admit an asymptotic expansion in inverse powers of N of whose coefficients are the Hurwitz numbers. Dubrovin and Yang [13] computed the cumulant generating function for the GUE, while Gisonni, Grava and Ruzza [24] calculated the generating function of the cumulants of the LUE.…”

Section: Introductionmentioning

confidence: 99%

Symmetric Function Theory and Unitary Invariant Ensembles

Jonnadula,

Keating,

Mezzadri

2020

Preprint

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Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices drawn from the Circular Unitary Ensemble and other Circular Ensembles related to the classical compact groups. The reason is that they enable the derivation of exact formulae, which then provide a route to calculating the large-matrix asymptotics of these quantities. We develop a parallel theory for the Gaussian Unitary Ensemble of random matrices, and other related unitary invariant matrix ensembles. This allows us to write down exact formulae in these cases for the joint moments of the traces and the joint moments of the characteristic polynomials in terms of appropriately defined symmetric functions. For the joint moments of the traces, we use the resulting formula to determine the rate of approach to the central limit theorem when the matrix size tends to infinity.

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“…Monotone Hurwitz theory has proved to be a useful tool with diverse applications [10,24,36,67,72], and its discovery has sparked a surge of interest in combinatorial deformations of classical Hurwitz numbers [3,4,19,27,28,30,52]. Although the subject has taken on a life of its own, monotone Hurwtz numbers were originally summoned from the void as a weapon with which to attack Conjecture 1.1.…”

Section: Stable Asymptoticsmentioning

confidence: 99%