Related papers: Hardy's paradox for multi-settings and high-dimens…
We investigate the entanglement and nonlocality properties of two random XX spin-1/2 critical chains, in order to better understand the role of breaking translational invariance to achieve nonlocal states in critical systems. We show that…
We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we can rederive known doubly weighted Hardy inequalities. Our…
We extend Hardy's uncertainty principle for a square integrable function and its Fourier transform to the multidimensional case using a symplectic diagonalization. We use this extension to show that Hardy's uncertainty principle is…
We consider the series expansion of the $L^p$-Hardy inequality of \cite{BFT2}, in the particular case where the distance is taken from an interior point of a bounded domain in $\mathbb{R}^n$ and $1<p\neq n$. For $p<n$ we improve it by…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Low dimensional quasiperiodic systems exhibit localization transitions by turning all quantum states localized after a critical quasidisorder. While certain systems with modified or constrained quasiperiodic potential undergo multiple…
We prove a variant of the multidimensional polynomial Szemer\'edi theorem of Bergelson and Leibman where one replaces polynomial sequences with other sparse sequences defined by functions that belong to some Hardy field and satisfy certain…
A conjecture of Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…
In literature on imprecise probability little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision…
We prove a suite of dynamical results, including exactness of the transformation and piecewise-analyticity of the invariant measure, for a family of continued fraction systems, including specific examples over reals, complex numbers,…
We study the properties of the set of marginal distributions of infinite translation-invariant systems in the 2D square lattice. In cases where the local variables can only take a small number $d$ of possible values, we completely solve the…
We develop criteria to detect three classes of nonlocality that have been shown by Wiseman et al. [Phys. Rev. Lett. 98, 140402 (2007)] to be nonequivalent: entanglement, EPR steering, and the failure of local hidden-variable theories. We…
Strong quantum nonlocality was introduced recently as a stronger manifestation of nonlocality in multipartite systems through the notion of local irreducibility in all bipartitions. Known existence results for sets of strongly nonlocal…
Severe impossibility results restrict the design of strategyproof random assignment mechanisms, and trade-offs are necessary when aiming for more demanding efficiency requirements, such as ordinal or rank efficiency. We introduce hybrid…
The geometric dimensionality of a physical system significantly impacts its fundamental characteristics. While experiments are fundamentally limited to the maximum of three spatial dimensions, there is a growing interest in harnessing…
We consider optimal interpolation of functions analytic in simply connected domains in the complex plane. By choosing a specific structure for the approximant, we show that the resulting first order optimality conditions can be interpreted…
We consider the twin paradox of special relativity in a universe with a compact spatial dimension. Such topology allows two twin observers to remain inertial yet meet periodically. The paradox is resolved by considering the relationship of…
We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the whole system,…
We extend the potential theory on almost minimzers from Part 1. We introduce so-called Hardy structures to study many classical operators using the tools from part 1. Furthermore, we show that for a naturally defined operator L, minimal…
We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a…