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…
Infinite linear patterns in sets of positive density
Felipe Hernández
In this article we describe all possible infinite linear configurations that can be found in a shift of any set of positive upper Banach density. This simultaneously generalizes Sz…
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 . W…
Multiple Polynomial Recurrence in Weyl Systems
Felipe Hernández
In this work we give a full characterization of sets of multiple polynomial recurrence in Weyl systems, which are ergodic unipotent affine transformations on products of tori and f…
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…