190 citations · 1.9k across the 70 of their papers we have counts for
4 papers · 1 filter
The Distribution of the Largest Eigenvalue in the Gaussian Ensembles
Craig A. Tracy, Harold Widom
The focus of this survey paper is on the distribution function for the largest eigenvalue in the finite N Gaussian ensembles (GOE,GUE,GSE) in the edge scaling limit of N->infinity.…
An Integral Operator Solution to the Matrix Toda Equations
Harold Widom
In previous work the author found solutions to the Toda equations that were expressed in terms of determinants of integral operators. Here it is observed that a simple variant yiel…
Asymptotics of a Class of Solutions to the Cylindrical Toda Equations
C. A. Tracy, H. Widom
The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, q_k(t), have the representation q_k(t) = log det(I-lambda K_k) - lo…
On Exact Solutions to the Cylindrical Poisson-Boltzmann Equation with Applications to Polyelectrolytes
C. A. Tracy, H. Widom
Using exact results from the theory of completely integrable systems of the Painleve/Toda type, we examine the consequences for the theory of polyelectrolytes in the (nonlinear) Po…