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We extend the quantum discord to continuous variable systems and evaluate Gaussian quantum discord C(\rho) for bipartite Gaussian states. In particular, for squeezed thermal states (STS), we explicitly maximize the extractable information…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
We prove a stability version of Harper's cube vertex isoperimetric inequality, showing that subsets of the cube with vertex boundary close to the minimum possible are close to (generalised) Hamming balls. Furthermore, we obtain a local…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
We study the large time behavior of solutions to a linear transmission problem in one space dimension. The problem at hand models a thermoelastic material with second sound confined by a purely elastic one. We shall characterize all…
The functional characterization of a measure, an essential but delicate aspect of Stein's method, is shown to be accessible for stable probability distributions on convex cones. This notion encompasses the usual stable distributions…
Max-stable processes provide natural models for the modelling of spatial extreme values observed at a set of spatial sites. Full likelihood inference for max-stable data is, however, complicated by the form of the likelihood function as it…
For an $n$-dimensional real-valued centered Gaussian random vector $(X_1,\ldots,X_n)$ with any covariance matrix, the following moment product conjecture is proved in this paper \[ \mathbb{E}\prod_{j=1}^nX_j^{2m_j}\geq…
Condorcet's paradox is a fundamental result in social choice theory which states that there exist elections in which, no matter which candidate wins, a majority of voters prefer a different candidate. In fact, even if we can select any $k$…
In a recent paper we described a novel approach to the detection and parameter estimation of a non-Gaussian stochastic background of gravitational waves. In this work we propose an improved version of the detection procedure, preserving…
Inertial particles in 2D driven by a Gaussian white noise forcing are considered. For two examples of the forcing (compressible and incompressible) upper and lower bounds are found for the mean number of caustics as a function of Stokes…
We establish finite-time last-iterate guarantees for vanilla stochastic gradient descent in co-coercive games under noisy feedback. This is a broad class of games that is more general than strongly monotone games, allows for multiple Nash…
It is shown that coherence resonance, a phenomenon in which regularity of noise-induced oscillations in nonlinear excitable systems is maximized at a certain optimal noise intensity, can be observed in quantum dissipative systems. We…
Gaussian boson sampling is a model of photonic quantum computing that has attracted attention as a platform for building quantum devices capable of performing tasks that are out of reach for classical devices. There is therefore significant…
Using Heisenberg's uncertainty principle it is shown that the gravitational stability condition for a crystalline vacuum cosmic space implies to obtain an equation formally equivalent to the relation first used by Gamow to predict the…
Boson Sampling represents a promising approach to obtain an evidence of the supremacy of quantum systems as a resource for the solution of computational problems. The classical hardness of Boson Sampling has been related to the so called…
This paper investigates the parareal algorithms for solving the stochastic Maxwell equations driven by multiplicative noise, focusing on their convergence, computational efficiency and numerical performance. The algorithms use the…
In this paper, we propose robust stochastic algorithms for solving convex compositional problems of the form $f(\E_\xi g(\cdot; \xi)) + r(\cdot)$ by establishing {\bf sub-Gaussian confidence bounds} under weak assumptions about the tails of…
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…
Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…