14 citations · 58 across the 16 of their papers we have counts for
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Equilibrium problem for the eigenvalues of banded block Toeplitz matrices
Steven Delvaux
We consider banded block Toeplitz matrices with block rows and columns. We show that under certain technical assumptions, the normalized eigenvalue counting measure of $T…
An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices
Steven Delvaux, Maurice Duits
We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit…
A graph-based equilibrium problem for the limiting distribution of non-intersecting Brownian motions at low temperature
Steven Delvaux, Arno B. J. Kuijlaars
We consider n non-intersecting Brownian motion paths with p prescribed starting positions at time t=0 and q prescribed ending positions at time t=1. The positions of the paths at a…
A phase transition for non-intersecting Brownian motions, and the Painleve II equation
Steven Delvaux, Arno B. J. Kuijlaars
We consider n non-intersecting Brownian motions with two fixed starting positions and two fixed ending positions in the large n limit. We show that in case of 'large separation' be…