Page personnelle de Laure Dumaz

Laure Dumaz

Laboratoire du Ceremade, Université Paris-Dauphine
Place du Maréchal De Lattre De Tassigny
75016 Paris

E-mail: dumaz@ceremade.dauphine.fr
Office: C 618
Office phone: +33 (0)1 44 05 41 95

I am working in probability theory. Since October 2015, I have been a CNRS researcher in Ceremade, in the university Paris-Dauphine.

Together with Guillaume Barraquand, we are organizing the working group "Random matrices et graphs" MEGA taking place in IHP. With Mathieu Lewin, we are organizing the working group ESCAPADE in Ceremade.

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:

Download here .

Research:

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

Publications and preprints:

Localization of the continuous Anderson Hamiltonian in 1-d , with Cyril Labbé. Probability Theory and Related Fields. 2018.

Riccati transform f'/f 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. 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.

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).