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Anderson localization for the -d Schrödinger operator with white noise potential
Laure Dumaz, Cyril Labbé
We consider the random Schrödinger operator on obtained by perturbing the Laplacian with a white noise. We prove that Anderson localization holds for this operator: al…
The delocalized phase of the Anderson Hamiltonian in -d
Laure Dumaz, Cyril Labbé
We introduce a random differential operator, that we call the operator, whose spectrum is given by the $\mbox{Sch}_τ$ point process introduced by Kritchevski, Valkó…
Localization crossover for the continuous Anderson Hamiltonian in -d
Laure Dumaz, Cyril Labbé
We investigate the behavior of the spectrum of the continuous Anderson Hamiltonian , with white noise potential, on a segment whose size is sent to infinity. We…
Operator level hard-to-soft transition for -ensembles
Laure Dumaz, Yun Li, Benedek Valkó
The soft and hard edge scaling limits of -ensembles can be characterized as the spectra of certain random Sturm-Liouville operators. It has been shown that by tuning the paramet…
The stochastic Airy operator at large temperature
Laure Dumaz, Cyril Labbé
It was shown in [J. A. Ramírez, B. Rider and B. Virág. J. Amer. Math. Soc. 24, 919-944 (2011)] that the edge of the spectrum of ensembles converges in the large limit to th…