| | |
| | |
Stat |
Members: 3667 Articles: 2'599'751 Articles rated: 2609
08 February 2025 |
|
| | | |
|
Article overview
| |
|
The circular law for signed random regular digraphs | Nicholas A. Cook
; | Date: |
2 Aug 2015 | Abstract: | We 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 |
|
|
No review found.
Did you like this article?
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.
|
| |
|
|
|