相关论文: Lamperti-type laws
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
We used the Density Functional formalism, in particular the Scaled Particle Theory, applied to a length-polydisperse hard-rectangular fluid to study its phase behavior as a function of the mean particle aspect ratio ($\kappa_0$) and…
The present paper provides exact expressions for the probability distributions of linear functionals of the two-parameter Poisson--Dirichlet process $\operatorname {PD}(\alpha,\theta)$. We obtain distributional results yielding exact forms…
We study the dynamics of a particle moving in one-dimensional Lorentz lattice-gas where particle performs mainly three different kinds of motion {\it viz} ballistic motion, diffusion and confinement. There are two different types of…
A classical fact of the theory of almost periodic functions is the existence of their asymptotic distributions. In probabilistic terms, this means that if $f$ is a Besicovitch almost periodic function and $V$ is a random variable uniformly…
This paper provides a probabilist point of view about some results in analytic number theory. The main tool is the family of Zeta laws, which is a consolation for the non-existence of an uniform law on the set of integers. We prove the…
The 2-dimensional density of states of an electron is studied for a Poissonian random distribution of point vortices carrying $\alpha$ flux in unit of the quantum of flux. It is shown that, for any given density of impurities, there is a…
The probabilistic study of the value-distributions of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a certain probability measure related to the value-distribution of the Lerch zeta-function.…
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…
We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further…
We consider a string with fixed endpoints where the mass density and/or the elastic coefficient vary in a self-affine way as function of position. It is demonstrated how the eigenvalues in the asymptotic limit are distributed. Scaling laws…
This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random…
This paper considers the limiting distribution of $\pi_{\lambda,\theta}$, the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance \cite{MR1626158}. In \cite{MR2519357} the large deviation principle…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although…
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…