286 citations · 587 across the 20 of their papers we have counts for
23 papers
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 Stirling-type formula for the distribution of the length of longest increasing subsequences
Folkmar Bornemann
The discrete distribution of the length of longest increasing subsequences in random permutations of integers is deeply related to random matrix theory. In a seminal work, Baik…
The Challenge of Sixfold Integrals: The Closed-Form Evaluation of Newton Potentials between Two Cubes
Folkmar Bornemann
The challenge of explicitly evaluating, in elementary closed form, the weakly singular sixfold integrals for potentials and forces between two cubes has been taken up at various pl…
A Jentzsch-Theorem for Kapteyn, Neumann, and General Dirichlet Series
Folkmar Bornemann
Comparing phase plots of truncated series solutions of Kepler's equation by Lagrange's power series with those by Bessel's Kapteyn series strongly suggest that a Jentzsch-type theo…
Efficient numerical evaluation of thermodynamic quantities on infinite (semi-)classical chains
Christian B. Mendl, Folkmar Bornemann
This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combin…
Finite size effects for spacing distributions in random matrix theory: circular ensembles and Riemann zeros
Folkmar Bornemann, Peter J. Forrester, Anthony Mays
According to Dyson's three fold way, from the viewpoint of global time reversal symmetry there are three circular ensembles of unitary random matrices relevant to the study of chao…
Numerical Methods for the Discrete Map
Folkmar Bornemann, Alexander Its, Sheehan Olver +1
As a basic example in nonlinear theories of discrete complex analysis, we explore various numerical methods for the accurate evaluation of the discrete map introduced by Agaf…
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…
Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles
N. S. Witte, F. Bornemann, P. J. Forrester
The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painlevé II transcendent and its as…
Automatic Deformation of Riemann-Hilbert Problems with Applications to the Painlevé II Transcendents
Georg Wechslberger, Folkmar Bornemann
The stability and convergence rate of Olver's collocation method for the numerical solution of Riemann-Hilbert problems (RHPs) is known to depend very sensitively on the particular…
On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity
Shuhuang Xiang, Folkmar Bornemann
We study the optimal general rate of convergence of the n-point quadrature rules of Gauss and Clenshaw-Curtis when applied to functions of limited regularity: if the Chebyshev coef…
Optimal Contours for High-Order Derivatives
Folkmar Bornemann, Georg Wechslberger
As a model of more general contour integration problems we consider the numerical calculation of high-order derivatives of holomorphic functions using Cauchy's integral formula. Bo…
On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators
Folkmar Bornemann
By applying an idea of Borodin and Olshanski [J. Algebra 313 (2007), 40-60], we study various scaling limits of determinantal point processes with trace class projection kernels gi…
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…
The Airy_1 process is not the limit of the largest eigenvalue in GOE matrix diffusion
Folkmar Bornemann, Patrik L. Ferrari, Michael Prähofer
Using a systematic approach to evaluate Fredholm determinants numerically, we provide convincing evidence that the Airy_1-process, arising as a limit law in stochastic surface grow…
On the Numerical Evaluation of Fredholm Determinants
Folkmar Bornemann
Some significant quantities in mathematics and physics are most naturally expressed as the Fredholm determinant of an integral operator, most notably many of the distribution funct…
A Model for Understanding Numerical Stability
Folkmar Bornemann
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is relat…
Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle
Folkmar Bornemann, Christian Rasch
We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplifi…
Runge-Kutta methods, trees, and Mathematica
Folkmar Bornemann
A simple and elementary proof of Butcher's theorem on the order conditions of Runge-Kutta methods is presented. It is based on a recursive definition of rooted trees and avoids com…