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**

On the Wasserstein distance between a hyperuniform point process and its mean, R. Butez, S. Dallaporta and D. Garcia-Zelada, preprint, hal-04544006

Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices, S. Belinschi, M. Capitaine, S. Dallaporta et M. Février, preprint, hal-03357405

Fluctuations of linear spectral statistics of deformed Wigner matrices, S. Dallaporta and M. Février, to appear in Séminaire de Probabilités, 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.

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.

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