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Random points in the unit ball of # n Guillaume Aubrun

Summary: Random points in the unit ball of # n
Guillaume Aubrun
Abstract. We show that two limit results from random matrix theory, due to
Mar#enko--Pastur and Bai--Yin, are also valid for matrices with independent
rows (as opposed to independent entries in the classical theory), when rows
are uniformly distributed on the unit ball of # n
p , under proper normalization.
Mathematics Subject Classification (2000). Primary 15A52, 52A21.
Keywords. # n
p spaces, random matrices, random vectors.
Let us start with the following classical results from Random Matrix Theory.
Let Z be a random variable such that
EZ = 0 and EZ 2 = 1. (1)
Consider an infinite array (Z ij ) of i.i.d. copies of Z. For each couple (n, N) of
integers, let G n,N be the N × n random matrix
G n,N = # 1
# N
Z ij # 1#i#N,1#j#n
. (2)


Source: Aubrun, Guillaume - Institut Camille Jordan, Université Claude Bernard Lyon-I


Collections: Mathematics