Related papers: r-Lah Distribution: Properties, Limit Theorems and…
In this article, we use the strong law of large numbers to give a proof of the Herschel-Maxwell theorem, which characterizes the normal distribution as the distribution of the components of a spherically symmetric random vector, provided…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
There exist a large literature on the application of $q$-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, $P_R(0,t)$,…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…
The paper deals with a new class of random walks strictly connected with the Pareto distribution. We consider stochastic processes in the sense of generalized convolution or weak generalized convolution following the idea given in [1]. The…
We present new stochastic geometry theorems that give bounds on the probability that $m$ random data classes all contain a point in common in their convex hulls. We apply these stochastic separation theorems to obtain bounds on the…
For the perimeter length $L_n$ and the area $A_n$ of the convex hull of the first $n$ steps of a planar random walk, this thesis study $n \to \infty$ mean and variance asymptotics and establish distributional limits. The results apply to…
There are many open questions pertaining to the statistical analysis of random objects, which are increasingly encountered. A major challenge is the absence of linear operations in such spaces. A basic statistical task is to quantify…
Waves propagate through disordered systems in a variety of regimes. There is a threshold of disorder beyond which waves become localized and transport becomes restricted. The intensity I of the wave transmitted through a system has a…
We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in [Vila et al., 2022, Bivariate Log-symmetric Models: Theoretical Properties and Parameter Estimation. Avaliable at…
We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
Transmission of the scalar field through the random medium, represented by the system of randomly distributed dielectric cylinders is calculated numerically. System is mapped to the problem of electronic transport in disordered…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
In this paper, we discuss the utilization of perturbed risk levels (PRLs) for the solution of chance-constrained problems via sampling-based approaches. PRLs allow the consideration of distributional ambiguity by rescaling the risk level of…
Over the last decades, impressive progresses have been made in many experimental domains, e.g. microscopic techniques such as single-particle tracking, leading to plethoric amounts of data. In a large variety of systems, from natural to…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…