相关论文: A Short Note on the Jensen-Shannon Divergence betw…
Although continuous symmetries may be more appealing, especially the local gauge ones, I argue that discrete symmetries may still play a fundamental role in shaping our understanding of the physics beyond the Standard Model. I exemplify…
Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d random variables chosen from a fixed probability distribution p of mean 0, variance 1 and finite higher moments. Previous work [BDJ,HM] showed that the…
Pinsker's widely used inequality upper-bounds the total variation distance $||P-Q||_1$ in terms of the Kullback-Leibler divergence $D(P||Q)$. Although in general a bound in the reverse direction is impossible, in many applications the…
The classic problems of testing uniformity of and learning a discrete distribution, given access to independent samples from it, are examined under general $\ell_p$ metrics. The intuitions and results often contrast with the classic…
We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving…
Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…
In this paper, we establish moderate deviations for the chemical distance in Bernoulli percolation. The chemical distance between two points is the length of the shortest open path between these two points. Thus, we study the size of random…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
We investigate existence and properties of discrete mixture representations $P_\theta =\sum_{i\in E} w_\theta(i) \, Q_i$ for a given family $P_\theta$, $\theta\in\Theta$, of probability measures. The noncentral chi-squared distributions…
We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the…
We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting…
We propose a simple yet powerful test statistic to quantify the discrepancy between two conditional distributions. The new statistic avoids the explicit estimation of the underlying distributions in highdimensional space and it operates on…
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…
Let $A_n$ be a random symmetric matrix with Bernoulli $\{\pm 1\}$ entries. For any $\kappa>0$ and two real numbers $\lambda_1,\lambda_2$ with a separation $|\lambda_1-\lambda_2|\geq \kappa n^{1/2}$ and both lying in the bulk…
Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is…
Multiplicity distributions of intermediate mass fragments (IMF) seen in intermediate energy heavy ion collisions have been of great interest in the last ten years. The distributions of single intermediate sized element are close to…
A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of…
Mutually uncorrelated random discrete events, manifesting a common basic process, are examined often in terms of their occurrence rate as a function of one or more of their distinguishing attributes, such as measurements of photon spectrum…
In heavy nuclei the spatial distribution of protons and neutrons is different. At CERN SPS energies production of $\pi^+$ and $\pi^-$ differs for $pp$, $pn$, $np$ and $nn$ scattering. These two facts lead to an impact parameter dependence…
We propose a novel approach for quantifying deviations from Gaussianity by leveraging the permutation Jensen-Shannon distance. Using stable distributions as a flexible framework, we analyze the effects of skewness and heavy tails in…