TY - JOUR

T1 - The rank of random regular digraphs of constant degree

AU - Litvak, Alexander E.

AU - Lytova, Anna

AU - Tikhomirov, Konstantin

AU - Tomczak-Jaegermann, Nicole

AU - Youssef, Pierre

N1 - Funding Information:
P.Y. was supported by grant ANR - 16-CE40-0024-01 . A significant part of this work was completed while the last three named authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, supported by NSF grant DMS-1440140 , and the first two named authors visited the institute. The hospitality of MSRI and of the organizers of the program on Geometric Functional Analysis and Applications is gratefully acknowledged.
Funding Information:
P.Y. was supported by grant ANR-16-CE40-0024-01. A significant part of this work was completed while the last three named authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, supported by NSF grant DMS-1440140, and the first two named authors visited the institute. The hospitality of MSRI and of the organizers of the program on Geometric Functional Analysis and Applications is gratefully acknowledged.

PY - 2018/10

Y1 - 2018/10

N2 - Let d be a (large) integer. Given n≥2d, let An be the adjacency matrix of a random directed d-regular graph on n vertices, with the uniform distribution. We show that the rank of An is at least n−1 with probability going to one as n grows to infinity. The proof combines the well known method of simple switchings and a recent result of the authors on delocalization of eigenvectors of An.

AB - Let d be a (large) integer. Given n≥2d, let An be the adjacency matrix of a random directed d-regular graph on n vertices, with the uniform distribution. We show that the rank of An is at least n−1 with probability going to one as n grows to infinity. The proof combines the well known method of simple switchings and a recent result of the authors on delocalization of eigenvectors of An.

KW - Random matrices

KW - Random regular graphs

KW - Rank

KW - Singularity probability

UR - http://www.scopus.com/inward/record.url?scp=85047378427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047378427&partnerID=8YFLogxK

U2 - 10.1016/j.jco.2018.05.004

DO - 10.1016/j.jco.2018.05.004

M3 - Article

AN - SCOPUS:85047378427

VL - 48

SP - 103

EP - 110

JO - Journal of Complexity

JF - Journal of Complexity

SN - 0885-064X

ER -