Page personnelle de Laure Dumaz

Laure Dumaz

Laboratoire du DMA, École Normale supérieure
45 rue d'Ulm
75005 Paris

E-mail: dumaz at dma.ens.fr
Office: Espace Cartan, C 20
Office phone: +33 (0)1 44 32 20 90

I am working in probability theory. I have been a CNRS researcher at the DMA within École Normale supérieure since September 2020. Additionally, since September 2021, I have been an associate professor in the DMA. Prior to this, from October 2015 to August 2020, I was affiliated with University Paris-Dauphine.

Together with Djalil Chafai, we are organizing the informal probability seminar of DMA.

I did my PhD under the supervision of Bálint Tóth and Wendelin Werner, defended in December 2012 (here is the manuscript (partially in French)).

Resume (in French):

Download here .

Research:

My current main research topics are random Schrödinger operators and random matrices, in particular the phenomenon of localization/delocalization. I have also been interested in SLE processes, conformal invariance, statistical models and near-criticality, and self-interacting processes.

Publications and preprints:

Anderson localization for the 1-d Schrödinger operator with white noise potential , with Cyril Labbé. Journal of Functional Analysis. 2024.
Localization crossover for the continuous Anderson Hamiltonian in 1-d , with Cyril Labbé. Inventiones mathematicae. 2024.

Simulation of three eigenvectors of the 1-d Schrödinger operator -d^2/dt^2 + B' (where B' is the white noise). Left one: the first eigenvector, middle one, 200th eigenvector and right one 700th eigenvector. We observe the transition from strongly localized to delocalized.

The delocalized phase of the Anderson Hamiltonian in 1-d , with Cyril Labbé. Annals of Probability. 2023.
Operator level hard-to-soft transition for beta-ensembles , with Yun Li and Benedek Valkó. Electron. J. Probab. 2021.
The stochastic Airy operator at large temperature , with Cyril Labbé. Annals of Applied Probability. 2022.
Localization of the continuous Anderson Hamiltonian in 1-d , with Cyril Labbé. Probability Theory and Related Fields. 2018.

Riccati transform f'/f (in black) of the first eigenvector f of the Schrödinger operator -d^2/dt^2 + B' (where B' is the white noise) and its approximation by diffusions (in blue and red). This eigenvector is localized around the explosions of the diffusions and growths/decays exponentially about this point.

Near-critical spanning forests and renormalization , with Stéphane Benoist and Wendelin Werner. arXiv:1503.08093 . 2015. Annals of Probability.

Image of a near-critical forest (a different color is associated to each cluster).
Click here for a simulation of the dynamics we are studying.

From Sine kernel to Poisson statistics , with Romain Allez. Electronic Journal of Probability. 2014.

Random matrices in non-confining potentials, with Romain Allez. arXiv:1404.5265 . Journal of Statistical Physics. 2014.

Tracy-Widom at high temperature, with Romain Allez. arXiv:1312.1283 . Journal of Statistical Physics. 2013.

Marginal densities of the "true" self-repelling motion , with Bálint Tóth. arXiv:1202.4327 . Stochastic Processes and their Applications. 2013.

A clever (self-repelling) Burglar . Electronic Journal of Probability. 2012.

The right tail exponent of the Tracy-Widom-beta distribution , with Bálint Virág. arXiv:1102.4818 . Annales de l'IHP. 2013.

Large deviations and path properties of the true self-repelling motion. arXiv:1105.2948 . Bulletin de la SMF . 2011.

Publication in applied mathematics :

Acoustic and geoacoustic inverse problems in randomly perturbed shallow-water environments, with Josselin Garnier and Guilhem Lepoultier. arXiv:1812.10141 . accepted in JASA. 2019.

Lecture notes

Lecture notes (in French) of a mini-course on Random matrices and graphs and some applications to correlation matrices given in Bordeaux (draft).