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The Eigenvalue Distribution of a Random Unipotent Matrix in Its Representation on Lines

✍ Scribed by Jason Fulman

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
120 KB
Volume
228
Category
Article
ISSN
0021-8693

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✦ Synopsis

The eigenvalue distribution 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 to 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 and Kirillov emerge.

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