49 citations · 237 across the 16 of their papers we have counts for
6 papers · 1 filter
On the number of zeros of linear combinations of independent characteristic polynomials of random unitary matrices
Yacine Barhoumi, Chris Hughes, Joseph Najnudel +1
We show that almost all the zeros of any finite linear combination of independent characteristic polynomials of random unitary matrices lie on the unit circle. This result is the r…
Random permutation matrices under the generalized Ewens measure
Christopher Hughes, Joseph Najnudel, Ashkan Nikeghbali +1
We consider a generalization of the Ewens measure for the symmetric group, calculating moments of the characteristic polynomial and similar multiplicative statistics. In addition,…
The characteristic polynomial of a random unitary matrix: a probabilistic approach
Paul Bourgade, Chris Hughes, Ashkan Nikeghbali +1
In this paper, we propose a probabilistic approach to the study of the characteristic polynomial of a random unitary matrix. We recover the Mellin Fourier transform of such a rando…
An arithmetic model for the total disorder process
C. P. Hughes, A. Nikeghbali, M. Yor
We prove a multidimensional extension of Selberg's central limit theorem for the logarithm of the Riemann zeta function on the critical line. The limit is a totally disordered proc…
On the distribution of lattice points in thin annuli
C. P. Hughes, Z. Rudnick
We show that the number of lattice points lying in a thin annulus has a Gaussian value distribution if the width of the annulus tends to zero sufficiently slowly as we increase the…
Mock-Gaussian Behaviour for Linear Statistics of Classical Compact Groups
C. P. Hughes, Z. Rudnick
We consider the scaling limit of linear statistics for eigenphases of a matrix taken from one of the classical compact groups. We compute their moments and find that the first few…