1999/05/24 by Jason Fulman, Fulman, Jason
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR
paper · pdf · doi:10.48550/arxiv.math/9905149
arxiv created 1999/05/24 · arxiv updated 2009/11/30
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..