The logarithmic law of random determinant Journal Article

Author(s): Bao, Zhigang; Pan, Guangming; Zhou, Wang
Article Title: The logarithmic law of random determinant
Affiliation IST Austria
Abstract: Consider the square random matrix An = (aij)n,n, where {aij:= a(n)ij , i, j = 1, . . . , n} is a collection of independent real random variables with means zero and variances one. Under the additional moment condition supn max1≤i,j ≤n Ea4ij <∞, we prove Girko's logarithmic law of det An in the sense that as n→∞ log | detAn| ? (1/2) log(n-1)! d/→√(1/2) log n N(0, 1).
Keywords: CLT for martingale; logarithmic law; random determinant
Journal Title: Bernoulli
Volume: 21
Issue 3
ISSN: 1350-7265
Publisher: Bernoulli Society for Mathematical Statistics and Probability  
Date Published: 2015-08-01
Start Page: 1600
End Page: 1628
DOI: 10.3150/14-BEJ615
Open access: yes (repository)