10 papers
Structure and Spectrum of Nonergodic Nilsystems
Felipe Hernández
We study Host-Kra factors and the spectral type of nilsystems, without assuming ergodicity. In the ergodic case, it is known that the spectral type splits into a discrete component…
Exponential Localization of Spatial Random Permutations in One Dimension
Reuben Drogin, Felipe Hernández
We consider a class of random permutations of the interval , in which points are typically displaced a distance . We show the cycles are localized on the scale ,…
Local limit theorems for random isometries of the plane
Reuben Drogin, Felipe Hernández
We consider a random walk on generated by successively applying independent random isometries, drawn from a fixed measure , to the point . Wh…
The threshold for quantum-classical correspondence is
Felipe Hernández, Daniel Ranard, C. Jess Riedel
In chaotic quantum systems, an initially localized quantum state can deviate strongly from the corresponding classical phase-space distribution after the Ehrenfest time $t_{\mathrm…
Lecture notes on Quantum Diffusion and Random Matrix Theory
Felipe Hernández
In joint work with Adam Black and Reuben Drogin, we develop a new approach to understanding the diffusive limit of the random Schrodinger equation based on ideas taken from random…
A simple bound on fluctuations in the 3D Coulomb gas
Alex Cohen, Felipe Hernández
The Coulomb gas models an interacting system of negatively charged particles. We give a new proof that, at sufficiently low temperature, smooth linear statistics $\sum_j φ(x_j)…