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Random Matrices and Brownian Motion†

Published online by Cambridge University Press:  12 September 2008

William M. Y. Goh  and
Eric Schmutz
William M. Y. Goh
Affiliation:
Department of Mathematics, Drexel University, Philadelphia, Pa. 19104
Eric Schmutz
Affiliation:
Department of Mathematics, Drexel University, Philadelphia, Pa. 19104
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Abstract

For T ∈ GLn (Fq), let Ωn (t, T) be the number of irreducible factors of degree less than or equal to nt in the characteristic polynomial of T. Let

and suppose T is chosen from G Ln(Fq) at random uniformly. We prove that the stochastic process ≺Zn(t)≻t∈[0, 1] converges to the standard Brownian motion process W(t), as n → ∞.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 2 , June 1993 , pp. 157 - 180
Copyright
Copyright © Cambridge University Press 1993

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