---
_id: '1506'
abstract:
- lang: eng
  text: 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).
article_processing_charge: No
arxiv: 1
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: Guangming
  full_name: Pan, Guangming
  last_name: Pan
- first_name: Wang
  full_name: Zhou, Wang
  last_name: Zhou
citation:
  ama: Bao Z, Pan G, Zhou W. The logarithmic law of random determinant. <i>Bernoulli</i>.
    2015;21(3):1600-1628. doi:<a href="https://doi.org/10.3150/14-BEJ615">10.3150/14-BEJ615</a>
  apa: Bao, Z., Pan, G., &#38; Zhou, W. (2015). The logarithmic law of random determinant.
    <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability.
    <a href="https://doi.org/10.3150/14-BEJ615">https://doi.org/10.3150/14-BEJ615</a>
  chicago: Bao, Zhigang, Guangming Pan, and Wang Zhou. “The Logarithmic Law of Random
    Determinant.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics
    and Probability, 2015. <a href="https://doi.org/10.3150/14-BEJ615">https://doi.org/10.3150/14-BEJ615</a>.
  ieee: Z. Bao, G. Pan, and W. Zhou, “The logarithmic law of random determinant,”
    <i>Bernoulli</i>, vol. 21, no. 3. Bernoulli Society for Mathematical Statistics
    and Probability, pp. 1600–1628, 2015.
  ista: Bao Z, Pan G, Zhou W. 2015. The logarithmic law of random determinant. Bernoulli.
    21(3), 1600–1628.
  mla: Bao, Zhigang, et al. “The Logarithmic Law of Random Determinant.” <i>Bernoulli</i>,
    vol. 21, no. 3, Bernoulli Society for Mathematical Statistics and Probability,
    2015, pp. 1600–28, doi:<a href="https://doi.org/10.3150/14-BEJ615">10.3150/14-BEJ615</a>.
  short: Z. Bao, G. Pan, W. Zhou, Bernoulli 21 (2015) 1600–1628.
date_created: 2018-12-11T11:52:25Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2025-09-23T13:59:56Z
day: '01'
department:
- _id: LaEr
doi: 10.3150/14-BEJ615
external_id:
  arxiv:
  - '1208.5823'
  isi:
  - '000356993100012'
intvolume: '        21'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1208.5823
month: '08'
oa: 1
oa_version: Preprint
page: 1600 - 1628
publication: Bernoulli
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
publist_id: '5671'
quality_controlled: '1'
status: public
title: The logarithmic law of random determinant
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 21
year: '2015'
...