Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3667
Articles: 2'599'751
Articles rated: 2609

08 February 2025
 
  » arxiv » 1508.0208

 Article overview



The circular law for signed random regular digraphs
Nicholas A. Cook ;
Date 2 Aug 2015
AbstractWe consider a large random matrix of the form $Y=Aodot X$, where $A$ the adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices, with $d=lfloor p n floor$ for some fixed $p in (0,1)$, and $X$ is an $n imes n$ matrix of iid centered Bernoulli signs (here $odot$ denotes the matrix Hadamard product). We prove that as $n ightarrow infty$, the empirical spectral distribution of $frac{1}{sqrt{d}}Y$ converges weakly in probability to the uniform measure on the unit disk in the complex plane. A key component of our proof is a lower bound on the least singular value of matrices of the form $Aodot X+B$, with $X$ as above, $B$ deterministic, and $A$ a deterministic 0/1 matrix satisfying certain "quasirandomness" conditions.
Source arXiv, 1508.0208
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.






ScienXe.org
» my Online CV
» Free

home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2025 - Scimetrica