11 citations · 14 across the 6 of their papers we have counts for
6 papers
A Riemann-Hilbert representation for Sobolev orthogonal polynomials
Alex Little
In this article we consider polynomials orthogonal with respect to the inner product $$\langle P,Q \rangle_S = \int_{\mathbb{R}}P(x)Q(x) \mathrm{e}^{-V(x)} \, \mathrm{d}x + λ\int_{…
Large deviations of the periodic Toda chain
Tamara Grava, Alice Guionnet, Karol K. Kozlowski +1
This work establishes a large deviation principle for the spectral measure of the Lax matrix associated to the periodic Toda chain of particles, subject to a generalised Gibbs…
A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type
Alex Little
We present a representation of skew-orthogonal polynomials of symplectic type () in terms of a matrix Riemann-Hilbert problem, for weights of the form where…
The complex elliptic Ginibre ensemble at weak non-Hermiticity: bulk spacing distributions
Thomas Bothner, Alex Little
We show that the distribution of bulk spacings between pairs of adjacent eigenvalue real parts of a random matrix drawn from the complex elliptic Ginibre ensemble is asymptotically…
The complex elliptic Ginibre ensemble at weak non-Hermiticity: edge spacing distributions
Thomas Bothner, Alex Little
The focus of this paper is on the distribution function of the rightmost eigenvalue for the complex elliptic Ginibre ensemble in the limit of weak non-Hermiticity. We show how the…
On the number of real eigenvalues of a product of truncated orthogonal random matrices
Alex Little, Francesco Mezzadri, Nick Simm
Let be chosen uniformly at random from the group of orthogonal matrices. Denote by the upper-left corner of , which we refer to…