Related papers: On free stable distributions
We define a Mellin amplitude for CFT$_1$ four-point functions. Its analytical properties are inferred from physical requirements on the correlator. We discuss the analytic continuation that is necessary for a fully nonperturbative…
In ref [math.ST/0411462] the notion of statistically dual distributions is introduced. The reconstruction of confidence density [AIP Conference Proceedings 803 (2005) 398] for the location parameter for several pairs of statistically dual…
In special relativity the mathematical expressions, defining physical observables as the momentum, the energy etc, emerge as one parameter (light speed) continuous deformations of the corresponding ones of the classical physics. Here, we…
Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis…
Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…
We introduce a large and flexible class of discrete tempered stable distributions, and analyze the domains of attraction for both this class and the related class of positive tempered stable distributions. Our results suggest that these are…
We introduce a general class of statistical-mechanics models, taking values in an abelian group, which includes examples of both spin and gauge models, both ordered and disordered. The model is described by a set of ``variables'' and a set…
In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…
Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the…
We completely determine the free infinite divisibility for the Boolean stable law which is parametrized by a stability index $\alpha$ and an asymmetry coefficient $\rho$. We prove that the Boolean stable law is freely infinitely divisible…
We study the distribution and various properties of exponential functionals of hypergeometric Levy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic…
This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin wave model, or width fluctuations of a two dimensional Edwards-Wilkinson…
We analyze one-dimensional motion of an overdamped classical particle in the presence of external disorder potential and an arbitrary driving force F. In thermodynamical limit the effective force-dependent mobility mu(F) is self-averaging,…
We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen `exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to…
Under the Riemann Hypothesis, we connect the distribution of $k$-free numbers with the derivative of the Riemann zeta-function at nontrivial zeros of $\zeta(s)$. Moreover, with additional assumptions, we prove the existence of a limiting…
In this article we study the influence of regularly varying probability measures on additive and multiplicative Boolean convolutions. We introduce the notion of Boolean subexponentiality (for additive Boolean convolution), which extends the…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivative. With…
In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the…
We study equilibrium states for an open class of non-uniformly expanding local homeomorphisms defined by a mild condition such that for some iterate each point admits at least one contracting inverse branch. We prove the existence and…