On the rightmost eigenvalue of non-Hermitian random matrices
Giorgio Cipolloni, László Erdős, Dominik Schröder, Yuanyuan Xu
Abstract
We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.
Topics & Concepts
MathematicsIndependent and identically distributed random variablesRandom matrixEigenvalues and eigenvectorsHermitian matrixTerm (time)InfinityAsymptotic expansionCircular lawMatrix (chemical analysis)Pure mathematicsApplied mathematicsMathematical analysisRandom variableStatisticsSum of normally distributed random variablesQuantum mechanicsComposite materialPhysicsMaterials scienceRandom Matrices and ApplicationsAdvanced Algebra and GeometryAdvanced Combinatorial Mathematics