The eigenvalue spacing of a random unipotent matrix in its action on lines
Combinatorics
2007-05-23 v1 Group Theory
Abstract
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach toward other asymptotics. For the case of all unipotent matrices, the proof gives a probabilistic interpretation to identities of Macdonald from symmetric function theory. For the case of upper triangular matrices over a finite field, connections between symmetric function theory and a probabilistic growth algorithm of Borodin emerge..
Cite
@article{arxiv.math/9905149,
title = {The eigenvalue spacing of a random unipotent matrix in its action on lines},
author = {Jason Fulman},
journal= {arXiv preprint arXiv:math/9905149},
year = {2007}
}