TY - JOUR

T1 - On sparse random combinatorial matrices

AU - Aigner-Horev, Elad

AU - Person, Yury

N1 - Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/11

Y1 - 2022/11

N2 - Let Qn,d denote the random combinatorial matrix whose rows are independent of one another and such that each row is sampled uniformly at random from the subset of vectors in {0,1}n having precisely d entries equal to 1. We present a short proof of the fact that [Formula presented], whenever ω(n1/2log3/2n)=d≤n/2. In particular, our proof accommodates sparse random combinatorial matrices in the sense that d=o(n) is allowed. We also consider the singularity of deterministic integer matrices A randomly perturbed by a sparse combinatorial matrix. In particular, we prove that [Formula presented], again, whenever ω(n1/2log3/2n)=d≤n/2 and A has the property that (1,−d) is not an eigenpair of A.

AB - Let Qn,d denote the random combinatorial matrix whose rows are independent of one another and such that each row is sampled uniformly at random from the subset of vectors in {0,1}n having precisely d entries equal to 1. We present a short proof of the fact that [Formula presented], whenever ω(n1/2log3/2n)=d≤n/2. In particular, our proof accommodates sparse random combinatorial matrices in the sense that d=o(n) is allowed. We also consider the singularity of deterministic integer matrices A randomly perturbed by a sparse combinatorial matrix. In particular, we prove that [Formula presented], again, whenever ω(n1/2log3/2n)=d≤n/2 and A has the property that (1,−d) is not an eigenpair of A.

KW - Random matrices

KW - Random perturbation

KW - Singularity

UR - http://www.scopus.com/inward/record.url?scp=85131834994&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2022.113017

DO - 10.1016/j.disc.2022.113017

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85131834994

SN - 0012-365X

VL - 345

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 11

M1 - 113017

ER -