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 |
URL: | |
DOI: | 10.3150/14-BEJ615 |
Open access: | yes (repository) |