Asymptotic study of eigenelements of a sequence of random selfadjoint operators

摘要: When (Tn) is a sequence of selfadjoint random operators on separable Hilbert space H converging almost surely to T, and converges in distribution operator U, we give explicitly the asymptotic joint all eigenelements Tn (eigenvalues, eigenvectors eigenprojectors) as function U. The results are obtained for real or complex operators, eigenvalues which arc simple not. They have many applications Multi-variate Analysis; example, studies Principal Component Analysis (real complex), Canonical Analysis, Discriminant Correspondence Functional models.