Related papers: Tempered distributions with discrete support and s…
We consider a strictly stationary and ergodic sequence of random elements taking values in some Hilbert space. Our target is to study the weak convergence of the discrete Fourier transforms under sharp conditions. As a side-result we obtain…
We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier…
We show that the flatness of a nonlinear discrete-time system can be checked by computing a unique sequence of involutive distributions. The well-known test for static feedback linearizability is included as a special case. Since the…
We investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a…
A method for constructing distributions on the non negative integers as discrete analogue of continuous distributions on the non negative real is presented. A justification of the definition of discrete self decomposable laws is provided.…
Dilworth's theorem. Every finite distributive lattice $D$ can be represented as the congruence lattice of a finite lattice $L$. We want: Every finite distributive lattice $D$ can be represented as the congruence lattice of a nice finite…
A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative equations. We show that the infinite series obtained by…
We consider the lattice of all the weak factorization systems on a given finite lattice. We prove that it is semidistributive, trim and congruence uniform. We deduce a graph theoretical approach to the problem of enumerating transfer…
The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…
Staggered fermion shift symmetries correspond to translations of the fermion field within the unit cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean dimensions can be related to a discrete subgroup of an $SU(4)$…
We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
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 consider the p-ordered characteristic function and its Fourier transform, the quasidistribution function, of squeezed coherent photons in a thermal state of photons and calculate the mean number and number variance of squeezed coherent…
In this paper we consider the stacking of isotonic regression and the method of rearrangement with the empirical estimator to estimate a discrete distribution with an infinite support. The estimators are proved to be strongly consistent…
Let G/H be a unimodular real spherical space which is either absolutely spherical or wave-front. It is shown that every tempered representation of G/H embeds into a relative discrete series of a boundary degeneration of G/H. If in addition…
A new method is proposed for the analysis of specular and off-specular reflectivity from supported lipid bilayers. Both thermal fluctuations and the "static" roughness induced by the substrate are carefully taken into account. Examples from…