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Sandrine Dallaporta


En français.



I am currently assistant professor at université de Poitiers and a member of LMA.

Research

I'm interested in random matrix theory. More precisely, I'm working on the non asymptotic behavior of the eigenvalues and singular values of certain large random matrices.

I did my PhD at institut de mathématiques de Toulouse, my advisor was Michel Ledoux. This thesis is entitled Some aspects of quantitative study of the counting function and the eigenvalues of random matrices. It is available here (the first three chapters are in French).

From 2012 to 2019, I was "agrégée préparatrice" at ENS Paris-Saclay and a member of CMLA.

Papers

Fluctuations of linear spectral statistics of deformed Wigner matrices, S. Dallaporta and M. Février, preprint, arXiv:1903.11324
This paper is interested in fluctuations of linear spectral statistics for deformed Wigner matrices around a deterministic equivalent. The fluctuations are proved to be Gaussian for smooth enough functions. Moreover, we provide a density argument inspired by Shcherbina and Johansson to extend the convergence of bias to less smooth functions.

Sparse recovery from extreme eigenvalues deviation inequalities, S. Dallaporta and Y. De Castro, to appear, ESAIM PS (pdf).
This paper provides a toolbox to derive sparse recovery guarantees from deviation inequalities on extreme eigenvalues of covariance matrices. This is then applied to Gaussian and Rademacher matrices.

Eigenvalue variance bounds for covariance random matrices, S. Dallaporta, MPRF 21 n°1 (2015), 145-175 (pdf).
In this paper, we give the proofs of some results for covariance matrices which were stated in the preceding paper.

Eigenvalue variance bounds for Wigner and covariance random matrices, S. Dallaporta, RMTA 1 n°3 (2012) (pdf).
This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices. These bounds are established for Gaussian matrices and then extended to large families of Wigner matrices by means of Erdös, Yau and Yin's Localization Theorem and Tao and Vu's Four Moment Theorem.  As a corollary, a bound on the expected rate of convergence of the empirical spectral measure towards the semicircle law in terms of 2-Wasserstein distance is derived. Analogous results for random covariance matrices are available.

A note on the central limit theorem for the eigenvalue counting function of Wigner matrices, S. Dallaporta and V. Vu, Electronic Communications in Probability 16 (2011), 314-322 (pdf).
This note establishes a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on results by Gustavsson, Tao and Vu and Erdös, Yau and Yin.

Unpublished note on the central limit theorem for the eigenvalue counting function of Wigner and covariance matrices, S. Dallaporta (pdf).
This unpublished note contains some details and complements on the first part of the preceding note.

The Q-process in a multitype branching process, S. Dallaporta and A. Joffe, Int. J. Pure Appl. Math. 42 n°2 (2008), 235-241 (pdf).
This note is concerned with multitype Galton-Watson processes. We study recurrence and transience properties of the Q-process, obtained from the initial process by conditionning on a very late extinction of the population.

Information

Email: sandrine.dallaporta_at_math.univ-poitiers.fr
Office: 0-15 building H3
Adress:
LMA - Université de Poitiers
Site du Futuroscope - Téléport 2
11 Boulevard Marie et Pierre Curie
Bâtiment H3 - TSA 61125
86073 POITIERS CEDEX 9
France