4 papers
Canonical Quantization of Neutral and Charged Static Black Hole as a Gravitational Atom
David Senjaya, Alejandro Saiz Rivera
The gravitational field is usually neglected in the calculation of atomic energy levels as its effect is much weaker than the electromagnetic field, but that is not the case for a…
Talagrand's inequality in planar Gaussian field percolation
Alejandro Rivera
Let f be a stationary isotropic non-degenerate Gaussian field on R^2. Assume that f = q * W where q is both C^2 and L^2 and W is the L^2 white noise on R^2. We extend a result by S…
A lower bound for the Bogomolny-Schmit constant for random monochromatic plane waves
Maxime Ingremeau, Alejandro Rivera
This note deals with nodal domains of random monochromatic plane waves. It was shown by Nazarov and Sodin that the expected number of such nodal domains included in a disk of radiu…
Weighted local Weyl laws for elliptic operators
Alejandro Rivera
Let be an elliptic pseudo-differential operator of order on a closed manifold of dimension , formally positive self-adjoint with respect to some positive…