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Asymptotic expansions relating to the lengths of longest monotone subsequences of involutions
Folkmar Bornemann
We study the distribution of the length of longest monotone subsequences in random (fixed-point free) involutions of integers as grows large, establishing asymptotic expans…
Asymptotic expansions relating to the distribution of the length of longest increasing subsequences
Folkmar Bornemann
We study the distribution of the length of longest increasing subsequences in random permutations of integers as grows large and establish an asymptotic expansion in powers…
A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge
Folkmar Bornemann
In a recent paper, Edelman, Guionnet and Péché conjectured a particular correction term of the smallest eigenvalue distribution of the Laguerre unitary ensemble (LUE) of o…
Singular Values and Evenness Symmetry in Random Matrix Theory
Folkmar Bornemann, Peter J. Forrester
Complex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular v…
The Singular Values of the GOE
Folkmar Bornemann, Michael La Croix
As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ens…
On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review
Folkmar Bornemann
In this paper we review and compare the numerical evaluation of those probability distributions in random matrix theory that are analytically represented in terms of Painlevé trans…
Asymptotic Independence of the Extreme Eigenvalues of GUE
Folkmar Bornemann
We give a short, operator-theoretic proof of the asymptotic independence (including a first correction term) of the minimal and maximal eigenvalue of the n \times n Gaussian Unitar…