Related papers: Asymptotics of the $k$-free diffraction measure vi…
Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. Tomography is a standard approach used to determine the form of an unknown state. Here we show that an alternative approach, based on…
We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on the general setting of finite translation-invariant metric…
Spectropolarimetry from the near IR to the far UV of light scattered by dust provides a valuable diagnostic of the dust composition, grain size distribution and spatial distribution. To facilitate the use of this diagnostic, we present…
The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $\beta\to 0$ under the assumption that random environment satisfies a certain…
We demonstrate a coherent quantum measurement for the determination of the degree of polarization (DOP). This method allows to measure the DOP in the presence of fast polarization state fluctuations, difficult to achieve with the typically…
We develop a theory for the analytic computation of the free energy of band insulators in the presence of a uniform and constant electric field. The two key ingredients are a perturbation-like expression of the Wannier-Stark energy spectrum…
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with…
We use the convolution method for arithmetic functions of several variables to deduce an asymptotic formula for the number of $k$-tuples of positive integers with components which are pairwise non-coprime and $\le x$. More generally, we…
We study "distance spheres": the set of points lying at constant distance from a fixed arbitrary subset $K$ of $[0,1]^d$. We show that, away from the regions where $K$ is "too dense" and a set of small volume, we can decompose $[0,1]^d$…
Estimating density functionals of analog sources is an important problem in statistical signal processing and information theory. Traditionally, estimating these quantities requires either making parametric assumptions about the underlying…
We give asymptotic approximations of the zeros of certain high degree polynomials. The zeros can be used to compute the filter coefficients in the dilation equations which define the compactly supported orthogonal Daubechies wavelets.…
We study the fluctuations of the light emitted by two identical incoherent point sources in a disordered environment. The intensity-intensity correlation function and the speckle contrast, obtained after proper temporal and configurational…
The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler…
We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the…
Absorption-free (also known as ``interaction-free'') measurement aims to detect the presence of an opaque object using a test particle without that particle being absorbed by the object. Here we consider semi-transparent objects which have…
We propose and analyze a method to detect and characterize the drift of a nonstationary quantum source. It generalizes a standard measurement for detecting phase diffusion of laser fields to quantum systems of arbitrary Hilbert space…
We discuss several examples of point processes (all taken from Hough, Krishnapur, Peres, Vir\'ag (2009)) for which the autocorrelation and diffraction measures can be calculated explicitly. These include certain classes of determinantal and…