Nonuniversality of fluctuations of outliers for Hermitian polynomials in a complex Wigner matrix and a spiked diagonal matrix
| Autor: | Mireille Capitaine |
|---|---|
| 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), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-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: | 2020 |
| Předmět: |
Statistics and Probability
Polynomial Algebra and Number Theory 010102 general mathematics Probability (math.PR) Free probability 01 natural sciences Hermitian matrix [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability Matrix (mathematics) Linearization Diagonal matrix Convergence (routing) FOS: Mathematics Discrete Mathematics and Combinatorics 0101 mathematics Statistics Probability and Uncertainty Random matrix Mathematics - Probability ComputingMilieux_MISCELLANEOUS Mathematics Mathematical physics |
| Zdroj: | Random Matrices: Theory and Applications Random Matrices: Theory and Applications, World Scientific, 2020, 09 (04), pp.2050013. ⟨10.1142/S2010326320500136⟩ Random Matrices: Theory and Applications, World Scientific, 2020, 09 (4), ⟨10.1142/S2010326320500136⟩ Random Matrices: Theory and Applications, 2020, 09 (04), pp.2050013. ⟨10.1142/S2010326320500136⟩ |
| ISSN: | 2010-3263 |
| DOI: | 10.1142/S2010326320500136⟩ |
| Popis: | International audience; We study the fluctuations associated to the a.s. convergence of the outliers established by Belinschi–Bercovici–Capitaine of an Hermitian polynomial in a complex Wigner matrix and a spiked deterministic real diagonal matrix. Thus, we extend the nonuniversality phenomenon established by Capitaine–Donati-Martin–Féral for additive deformations of complex Wigner matrices, to any Hermitian polynomial. The result is described using the operator-valued subordination functions of free probability theory. |
| Databáze: | OpenAIRE |
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