14 papers
On the structure of polynomial multicorrelation sequences arising from nilpotent actions
Jovan Andreevski, Felipe Hernández
We prove that every polynomial multicorrelation sequence arising from nilpotent actions admits a decomposition into a generalized nilsequence and a null-sequence. This resolves a l…
Infinite prime sumsets in structured and -uniform sets
Felipe Hernández, Tristán Radić
By introducing new ergodic-theoretic techniques in nilsystems, we determine which infinite sumset configurations occur in -uniform and Nil-Bohr sets. To be more precise, ou…
Quantum Chaos and Quantum Optimal Transport
Jordan Cotler, Felipe Hernández
Chaos in classical systems can be characterized by Lyapunov exponents that measure the exponential divergence of nearby trajectories, but directly extending this framework to quant…
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)…
On density analogs of Hindman's finite sums theorem
Felipe Hernández, Ioannis Kousek, Tristán Radić
For any set of natural numbers with positive upper Banach density, we show the existence of an infinite set and sequences …
An Egorov Theorem for Wasserstein Distances
Jordan Cotler, Felipe Hernández
We prove a new version of Egorov's theorem formulated in the Schrödinger picture of quantum mechanics, using the -Wasserstein metric applied to the Husimi functions of quantum s…
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…
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…
On recurrence for -Weyl systems
Sebastián Donoso, Felipe Hernández, Alejandro Maass
We study the topological recurrence phenomenon of actions of locally compact abelian groups on compact metric spaces. In the case of -actions we develop new technique…