The eigenvalue spacing of a random unipotent matrix in its action on lines

Preprint

24 May 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/9905149

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..

Keywords

SYMMETRIC FUNCTION
EIGENVALUE SPACING
RANDOM UNIPOTENT
UNIPOTENT MATRIX
ACTION ON LINES
PERMUTATION
ALGORITHM
MATRICES

All Related Versions

Version 1, 1999-05-24, ArXiv

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