Spectral properties of polynomials in independent Wigner and deterministic matrices
| Autor: | Mireille Capitaine, Serban T. Belinschi |
|---|---|
| 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), 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) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Polynomial
Pure mathematics Probability (math.PR) 010102 general mathematics Asymptotic distribution Free probability 01 natural sciences Hermitian matrix [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability FOS: Mathematics Almost surely 0101 mathematics Random matrix ComputingMilieux_MISCELLANEOUS Analysis Eigenvalues and eigenvectors Mathematics - Probability 15A18 15B52 60B20 46L54 Mathematics Probability measure |
| Zdroj: | Journal of Functional Analysis Journal of Functional Analysis, Elsevier, 2017, 273 (12), pp.3901-3963. ⟨10.1016/j.jfa.2017.07.010⟩ Journal of Functional Analysis, 2017, 273 (12), pp.3901-3963. ⟨10.1016/j.jfa.2017.07.010⟩ |
| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1016/j.jfa.2017.07.010⟩ |
| Popis: | On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interval lying at some distance from the supports of a sequence of deterministic probability measures, which is computed with the tools of free probability. On the other hand, we establish the strong asymptotic freeness of independent Wigner matrices and any family of deterministic matrices with strong limiting distribution. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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