Výsledky vyhledávání - "Mireille Capitaine"

Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices

Autor: Guillaume Cébron, Mireille Capitaine, Serban Belinschi, Charles Bordenave

Publikováno v: Electronic Journal of Probability
Electronic Journal of Probability, 2021, 26, ⟨10.1214/21-EJP666⟩
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2021, 26 (none), ⟨10.1214/21-EJP666⟩
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2021, 26, ⟨10.1214/21-EJP666⟩

We consider a square random matrix of size $N$ of the form $P(Y,A)$ where $P$ is a noncommutative polynomial, $A$ is a tuple of deterministic matrices converging in $\ast$-distribution, when $N$ goes to infinity, towards a tuple $a$ in some $\mathcal

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4ff451ed2f37abb67b01666c418af66f
https://hal.science/hal-03357298/document

Zobrazit plný text záznamu

Nonuniversality of fluctuations of outliers for Hermitian polynomials in a complex Wigner matrix and a spiked diagonal matrix

Autor: Mireille Capitaine

Publikováno v: 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⟩

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 matri

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3845cac74fbf816e3de14cd2a82b12b0
https://hal.archives-ouvertes.fr/hal-03038525

Zobrazit plný text záznamu

Outlier Eigenvalues for Deformed I.I.D. Random Matrices

Autor: Mireille Capitaine, Charles Bordenave

Publikováno v: Communications on Pure and Applied Mathematics
Communications on Pure and Applied Mathematics, Wiley, 2016, 69 (11), pp.2131-2194. ⟨10.1002/cpa.21629⟩
Communications on Pure and Applied Mathematics, 2016, 69 (11), pp.2131-2194. ⟨10.1002/cpa.21629⟩

We consider a square random matrix of size N of the form A + Y where A is deterministic and Y has iid entries with variance 1/N. Under mild assumptions, as N grows, the empirical distribution of the eigenvalues of A+Y converges weakly to a limit prob

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::674caac7c4fe829ec64c9c5d4bfc08a0
https://doi.org/10.1002/cpa.21629

Zobrazit plný text záznamu

Séminaire de probabilités XLIX

Publikováno v: Donati-Martin, Catherine; Lejay, Antoine; Rouault, Alain. Springer, 2215, 2018, Lecture notes in mathematics, ⟨10.1007/978-3-319-92420-5⟩
Lecture Notes in Mathematics ISBN: 9783319924199
Donati-Martin, Catherine; Lejay, Antoine; Rouault, Alain. 2215, Springer, 2018, Lecture notes in mathematics, ⟨10.1007/978-3-319-92420-5⟩

International audience

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6356160ea13a12ec9ee1746db4fbc917
https://inria.hal.science/hal-01931202

Zobrazit plný text záznamu

Non universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices

Autor: Mireille Capitaine, Catherine Donati-Martin

Publikováno v: 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⟩

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 matr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10e1600c18273cca4eae68d7a706ce19

Zobrazit plný text záznamu

Limiting Eigenvectors of Outliers for Spiked Information-Plus-Noise Type Matrices

Autor: Mireille Capitaine

Publikováno v: Séminaire de Probabilités XLIX ISBN: 9783319924199

We consider an Information-Plus-Noise type matrix where the Information matrix is a spiked matrix. When some eigenvalues of the random matrix separate from the bulk, we study how the corresponding eigenvectors project onto those of the spikes. Note t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7984110068e464aa0cbfbb7648cd92f4
https://doi.org/10.1007/978-3-319-92420-5_4

Zobrazit plný text záznamu

On the outlying eigenvalues of a polynomial in large independent random matrices

Autor: Hari Bercovici, Mireille Capitaine, Serban T. Belinschi

Publikováno v: Preliminary version. Comments/observations/corrections are welcome!. 2017
International Mathematics Research Notices
International Mathematics Research Notices, Oxford University Press (OUP), 2021, 2021 (4), pp.2588-2641. ⟨10.1093/imrn/rnz080⟩
International Mathematics Research Notices, Oxford University Press (OUP), 2019, ⟨10.1093/imrn/rnz080⟩
International Mathematics Research Notices, 2021, 2021 (4), pp.2588-2641. ⟨10.1093/imrn/rnz080⟩

Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A\_N,B\_N)$, where $A\_N$ and $B\_N$ are independent Hermitian random matrices and the d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bde419d0a2535186c395003d1dc9d95b
http://arxiv.org/abs/1703.08102

Zobrazit plný text záznamu

OUTLIERS IN THE SPECTRUM OF LARGE DEFORMED UNITARILY INVARIANT MODELS

Autor: Maxime Fevrier, Hari Bercovici, Mireille Capitaine, Serban T. Belinschi

Publikováno v: Annals of Probability
Annals of Probability, Institute of Mathematical Statistics, 2017, 45 (6A), pp.3571-3625. ⟨10.1214/16-AOP1144⟩
Annals of Probability, Institute of Mathematical Statistics, 2017, 45 (6A), pp.3571-3625
Annals of Probability, 2017, 45 (6A), pp.3571-3625. ⟨10.1214/16-AOP1144⟩
Ann. Probab. 45, no. 6A (2017), 3571-3625

We investigate the asymptotic behavior of the eigenvalues of the sum A+U*BU, where A and B are deterministic N by N Hermitian matrices having respective limiting compactly supported distributions \mu, \nu, and U is a random N by N unitary matrix dist

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eb7558f51f36ca7aca9f1687021c8b96
https://hal.archives-ouvertes.fr/hal-01095551v2/file/Unitary-April-2015.pdf

Zobrazit plný text záznamu

Spectral properties of polynomials in independent Wigner and deterministic matrices

Autor: Mireille Capitaine, Serban T. Belinschi

Publikováno v: 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⟩

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 determinis

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e87a2caaad8a431db7d622a5c505b237
http://arxiv.org/abs/1611.07440

Zobrazit plný text záznamu

Fluctuations at the edges of the spectrum of the full rank deformed GUE

Autor: Mireille Capitaine, Sandrine Péché

Publikováno v: Probability Theory and Related Fields
Probability Theory and Related Fields, 2016, 165 (1), pp.117-161. ⟨10.1007/s00440-015-0628-6⟩
Probability Theory and Related Fields, Springer Verlag, 2016, 165 (1), pp.117-161. ⟨10.1007/s00440-015-0628-6⟩

We consider a full rank deformation of the GUE $W_N+A_N$ where $A_N$ is a full rank Hermitian matrix of size $N$ and $W_N$ is a GUE. The empirical eigenvalue distribution $\mu_{A_N}$ of $A_N$ converges to a probability distribution $\nu$. We identify

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8aeb329d5026c0e2800ca85cc5d9b8d6
https://hal.science/hal-01011501

Zobrazit plný text záznamu

Vyhledávací nástroje:

Upřesnit hledání