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. Letand 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 → ∞.
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