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We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
The connection between fundamental interactions acting in molecules in a fluid and macroscopically measured properties, such as the viscosity between colloidal particles coated with polymers, is studied here. The role that hydrodynamic and…
Three-body systems that are continuously squeezed from a three-dimensional (3D) space into a two-dimensional (2D) space are investigated. Such a squeezing can be obtained by means of an external confining potential acting along a single…
Entanglement between two free bosonic modes can be determined via detection of each mode by different observers and then observing the correlations between their measurements. We show that such entanglement is degraded as a function of time…
Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on…
The aim of this paper is to provide the mathematical framework for analyzing the possibility of rendering one dimensional objects visible with difficulty and ultimately invisible,by changing the experimental conditions to which they are…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
We develop an intensive embedding for visualizing the space of all predictions for probabalistic models, using replica theory. Our embedding is isometric (preserves the distinguishability between models) and faithful (yields low-dimensional…
Glassiness occurs when disorder and frustration cause local degrees of freedom to freeze despite the lack of long-range order. In systems of interacting bosons, such glassiness may involve a purely quantum degree of…
A class of extra dimensional models with a warped metric predict tunneling of a massive particle localized on our brane and escaping into additional dimensions. The experimental signature of this effect is the disappearance of the particle…
Let $n$ particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a specific case of Brownian motion constrained to stay inside a Weyl chamber; the Weyl group for this…
We study the distances and gravitational lensing in spherically symmetric inhomogeneous cosmological models consisting of inner and outer homogeneous regions which are connected by a single shell or double shells at the redshift $z_1 \sim…
We study fundamental characteristics for the connectivity of multi-hop D2D networks. Devices are randomly distributed on street systems and are able to communicate with each other whenever their separation is smaller than some connectivity…
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2<d<4 this disorder is a relevant perturbation that drives the system to a new…
Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…
In recent years there has been a lot of interest in the study of isometry invariant Poisson processes of $k$-flats in $d$-dimensional hyperbolic space $\mathbb{H}^d$, for $0\le k\le d-1$. A phenomenon that has no counterpart in euclidean…
We present the results of weak gravitational lensing statistics in four different cosmological $N$-body simulations. The data has been generated using an algorithm for the three-dimensional shear, which makes use of a variable softening…
An $(n,k)$-Poisson Multinomial Distribution (PMD) is the distribution of the sum of $n$ independent random vectors supported on the set ${\cal B}_k=\{e_1,\ldots,e_k\}$ of standard basis vectors in $\mathbb{R}^k$. We prove a structural…
In this paper we investigate the phase structure of a (1+1) and (3+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($\mu_B$), isospin ($\mu_I$) and chiral isospin ($\mu_{I5}$) chemical potentials. It is…
We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases (MUBs) for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite and…