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This short note is a supplement to [1], in which the total variation of graph distributional signals is introduced and studied. We introduce a different formulation of total variation and relate it to the notion of edge centrality. The…
In this note, we study asymptotic zero distribution of multivariable full system of random polynomials with independent Bernoulli coefficients. We prove that with overwhelming probability their simultaneous zeros sets are discrete and the…
Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves the convexity of the random multifunction. We provide several…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…
Some properties of the inverse of the Normal distribution are studied. Its derivatives, integrals and asymptotic behavior are presented.
This paper studies the local spacings of deformations of the Riemann zeta function under certain averaging and differencing operations. For real h it considers A_h(s)= 1/2(xi(s+h)+ xi(s-h)) and B_h(s)=1/(2i)(xi(s+h)-xi(s-h)), where xi(s) is…
In this paper we find the partial sums of two kinds normalized Wright functions and the partial sums of Alexander transform of these normalized Wright functions.
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
Numerical investigations around a transformation of Landau's formula suggest certain statistical regularities in the distribution of zeros of the Riemann zeta function.
Motivated by applications in Bayesian analysis we introduce a multidimensional beta distribution in an ordered simplex. We study properties of this distribution and connect them with the generalized incomplete beta function. This function…
Let f_1,f_2,..., be functions chosen independently and uniformly from the set of all functions from a set of cardinality n into itself. Let g_t be the composition of the first t functions, and let T be the smallest t for which g_t is…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between $L_2$-small ball asymptotics of the transformed function and of the original one. Also the explicit…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
We characterize microlocal regularity of Colombeau generalized functions by an appropriate extension of the classical notion of micro-ellipticity to pseudodifferential operators with slow scale generalized symbols. Thus we obtain an…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…
The present paper examines the behavior of Shift-insertion sort (insertion sort with shifting) for normal distribution inputs and is in continuation of our earlier work on this new algorithm for discrete distribution inputs, namely,…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…