Related papers: On Boolean selfdecomposable distributions
We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the…
We derive a necessary and sufficient condition for the sum of M independent continuous random variables modulo 1 to converge to the uniform distribution in L^1([0,1]), and discuss generalizations to discrete random variables. A consequence…
The subject is partial resolution of singularities. Given an algebraic variety X (not necessarily equidimensional) in characteristic zero (or, more generally, a pair (X,D), where D is a divisor on X), we construct a functorial…
Determining the spin of any new particle is critical in identifying the true theory among various extensions of the Standard Model (SM). The degree of $Z$-boson polarization in any two-body decay process $A\to B Z$ is sensitive to the spin…
Generalised parton distributions are instrumental to study both the three-dimensional structure and the energy-momentum tensor of the nucleon, and motivate numerous experimental programmes involving hard exclusive measurements. Based on a…
From a new class of q-deformed coherent states we introduce a generalization of the Euler probability distribution for which the main statistical parameters are obtained explicitly. As application, we discuss the corresponding photon…
We prove a long-standing conjecture which characterises the Ewens-Pitman two-parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following property: for each $n = 2,3, >...$, if one…
We study Boolean stable laws, $\mathbf{b}_{\alpha,\rho}$, with stability index $\alpha$ and asymmetry parameter $\rho$. We show that the classical scale mixture of $\mathbf{b}_{\alpha,\rho}$ coincides with a free mixture and also a monotone…
We study the zeroes of a family of random holomorphic functions on the unit disc, distinguished by their invariance with respect to the hyperbolic geometry. Our main finding is a transition in the limiting behaviour of the number of zeroes…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
We derive asymptotic normality of kernel type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider the so called super smooth case where the characteristic…
We show that the embeddability relations for countable quandles and for countable fields of any given characteristic other than 2 are maximally complex in a strong sense: they are invariantly universal. This notion from the theory of Borel…
We study theoretically in the present work the self-assembly of molecules in an open system, which is fed by monomers and depleted in partial or complete clusters. Such a scenario is likely to occur for example in the context of viral…
The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with a given temperature. We give a novel characterization of this family as the unique one satisfying independence for…
Scale invariant scattering suggests that all Bernoulli numbers B_{2n} can be naturally partitioned, i.e., written as particular finite sums of same-signed, monotonic, rational numbers. Some properties of these rational numbers are discussed…
We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by $F_1 = 1, F_2 = 2$ and $F_{n+1} = F_n + F_{n-1}$, every positive integer can be written uniquely as a sum of…
We prove Holder regularity for solutions of non divergence integro-differential equations with non necessarily even kernels. The even/odd decomposition of the kernel can be understood as a sum of a diffusion and a drift term. In our case we…
The paper is devoted to infinite Bernoulli convolutions generated by positive multigeometric series and to probability distributions of random variables whose digits in an even integer base-$s$ expansion with two redundant digits form a…
The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…
Let $\cP_n$ be the space of homogeneous polynomials of degree $n$ on $\bbR^{m+1}$. We consider the asymptotic behavior of some coefficients relating to the decomposition of $\cP_n$ into the sum of $\SO(m+1)$-irreducible components. Using…