Non universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices
| Autor: | Mireille Capitaine, Catherine Donati-Martin |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Pure mathematics Nonuniversality Gaussian eigenvectors Poincaré inequality 15A18 60F05 01 natural sciences 010104 statistics & probability symbols.namesake Matrix (mathematics) 60F05 FOS: Mathematics Outliers Fluctuations 0101 mathematics Eigenvalues and eigenvectors ComputingMilieux_MISCELLANEOUS Mathematics 46L54 010102 general mathematics Mathematics::Rings and Algebras Probability (math.PR) 15A52 Block matrix 16. Peace & justice Hermitian matrix [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Outlier symbols Random matrices Free probability. Mathematics Subject Classification 2000: 15A18 60B12 Random matrix Mathematics - Probability |
| Zdroj: | ALEA : Latin American Journal of Probability and Mathematical Statistics ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, In press ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2021, 18 (1), pp.129-165. ⟨10.30757/ALEA.v18-07⟩ ALEA : Latin American Journal of Probability and Mathematical Statistics, 2021, 18 (1), pp.129-165. ⟨10.30757/ALEA.v18-07⟩ |
| ISSN: | 1980-0436 |
| DOI: | 10.48550/arxiv.1807.07773 |
| Popis: | In this paper, we investigate the fluctuations of a unit eigenvector associated to an outlier in the spectrum of a spiked $N\times N$ complex Deformed Wigner matrix $M_N$: $M_N =W_N/\sqrt{N} + A_N$ where $W_N$ is an $N \times N$ Hermitian Wigner matrix whose entries have a law $\mu$ satisfying a Poincar\'e inequality and the matrix $A_N$ is a block diagonal matrix, with an eigenvalue $\theta$ of multiplicity one, generating an outlier in the spectrum of $M_N$. We prove that the fluctuations of the norm of the projection of a unit eigenvector corresponding to the outlier of $M_N$ onto a unit eigenvector corresponding to $\theta$ are not universal. Comment: accepted for publication in Latin American Journal of Probability and Mathematical Statistics |
| Databáze: | OpenAIRE |
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