Spectrum of high-dimensional sample covariance and related matrices: a selective review

DOI10.1007/978-981-99-9994-1_2MaRDI QIDQ6645567

Arup Bose, Monika Bhattacharjee

Publication date: 28 November 2024

zbMATH Keywords

Stieltjes transformcovariance matrixmatrix polynomialfactor modelhigh-dimensional time seriesfree cumulantWigner matrixtest of independencefree independencelinear spectral statisticsspiked covariance matrixbanded matrixnon-commutative probabilityautocovariance matrixMarčenko-Pastur lawjoint convergenceseparable covariance matrixcircular variableorder determinationgeneralized covariance matrixsub-exponential decayTracy-Widom lawscompound free Poisson lawcross-covariance matrixgraphical inferencecross-covariance variableelliptic variableKendall's \(\tau\) matrixself-adjoint variablesemi-circular law/variableSpearman's \(\rho\) matrixtapered and banded matrices

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Free probability and free operator algebras (46L54) Stochastic analysis (60Hxx)

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