6533b85cfe1ef96bd12bca66

RESEARCH PRODUCT

The rank of random regular digraphs of constant degree

Konstantin TikhomirovPierre YoussefNicole Tomczak-jaegermannAlexander E. LitvakAnna Lytova

subject

Statistics and ProbabilityControl and OptimizationUniform distribution (continuous)General Mathematics0102 computer and information sciencesrandom matrices01 natural sciencesCombinatoricsIntegerFOS: Mathematics60B20 15B52 46B06 05C80Rank (graph theory)Adjacency matrix0101 mathematicsEigenvalues and eigenvectorsMathematicsNumerical AnalysisAlgebra and Number TheoryDegree (graph theory)Applied MathematicsProbability (math.PR)010102 general mathematicsrandom regular graphssingularity probabilityrank010201 computation theory & mathematicsRegular graphRandom matrixMathematics - Probability

description

Abstract Let d be a (large) integer. Given n ≥ 2 d , let A n be the adjacency matrix of a random directed d -regular graph on n vertices, with the uniform distribution. We show that the rank of A n 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 A n .

yearjournalcountryeditionlanguage
2018-01-01Journal of Complexity
https://doi.org/10.1016/j.jco.2018.05.004