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The Circular Law for random regular digraphs

Publication ,  Journal Article
Cook, N
Published in: Annales De L Institut Henri Poincare B Probability and Statistics
January 1, 2019

Let logC n ≤ d ≤ n/2 for a sufficiently large constant C > 0 and let An denote the adjacency matrix of a uniform random d-regular directed graph on n vertices. We prove that as n tends to infinity, the empirical spectral distribution of An, suitably rescaled, is governed by the Circular Law. A key step is to obtain quantitative lower tail bounds for the smallest singular value of additive perturbations of An

Duke Scholars

Published In

Annales De L Institut Henri Poincare B Probability and Statistics

DOI

ISSN

0246-0203

Publication Date

January 1, 2019

Volume

55

Issue

4

Start / End Page

2111 / 2167

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

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ICMJE
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Cook, N. (2019). The Circular Law for random regular digraphs. Annales De L Institut Henri Poincare B Probability and Statistics, 55(4), 2111–2167. https://doi.org/10.1214/18-AIHP943
Cook, N. “The Circular Law for random regular digraphs.” Annales De L Institut Henri Poincare B Probability and Statistics 55, no. 4 (January 1, 2019): 2111–67. https://doi.org/10.1214/18-AIHP943.
Cook N. The Circular Law for random regular digraphs. Annales De L Institut Henri Poincare B Probability and Statistics. 2019 Jan 1;55(4):2111–67.
Cook, N. “The Circular Law for random regular digraphs.” Annales De L Institut Henri Poincare B Probability and Statistics, vol. 55, no. 4, Jan. 2019, pp. 2111–67. Scopus, doi:10.1214/18-AIHP943.
Cook N. The Circular Law for random regular digraphs. Annales De L Institut Henri Poincare B Probability and Statistics. 2019 Jan 1;55(4):2111–2167.
Journal cover image

Published In

Annales De L Institut Henri Poincare B Probability and Statistics

DOI

ISSN

0246-0203

Publication Date

January 1, 2019

Volume

55

Issue

4

Start / End Page

2111 / 2167

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics