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Sandrine Dallaporta


En français.



I am currently "agrégée préparatrice" at ENS Cachan and a member of CMLA.

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).


Papers

Restricted Isometry Constants for Gaussian and Rademacher matrices, S. Dallaporta and Y. De Castro, preprint (pdf).
In this paper, deviation inequalities for extreme eigenvalues of covariance matrices are used to get bounds on constants appearing in the Restricted Isometry Property.

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Unpublished note on the central limit theorem for the eigenvalue counting function of Wigner and covariance matrices, S. Dallaporta (pdf).
This unpublished note contains some details and complements on the first part of the preceding note.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_cmla.ens-cachan.fr
Office : 104 building Cournot 1st floor
Adress :
CMLA - ENS Cachan
61 avenue du Président Wilson
94235 CACHAN Cedex
France