Related papers: A dynamical characterization of Poisson-Dirichlet …

Let $p_1 \ge p_2 \ge \dots$ be the prime factors of a random integer chosen uniformly from $1$ to $n$, and let $$ \frac{\log p_1}{\log n}, \frac{\log p_2}{\log n}, \dots $$ be the sequence of scaled log factors. Billingsley's Theorem…

We extend a theorem of Maa, Pearl, and Bartoszynski, which links equality of interpoint distance distributions to equality of underlying multivariate distributions, beyond the restrictive class of homogeneous, translation-invariant distance…

Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $\sigma$-finite intensity…

We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…

A constrained diffusive random walk of n steps and a random flight in Rd, which can be expressed in the same terms, were investigated independently in recent papers. The n steps of the walk are identically and independently distributed…

One of the main contributions of this paper is to illustrate how large deviation theory can be used to determine the equilibrium distribution of a basic droplet model that underlies a number of important models in material science and…

Rubinstein and Sarnak investigated systems of inequalities of the form pi(x;q,a_1) > ... > pi(x;q,a_r), where pi(x;q,a) denotes the number of primes up to x that are congruent to a mod q. They showed, under standard hypotheses on the zeros…

For a base $b\geq 2$ and a set of digits $\mathcal{A}\subset \{0,...,b-1\}$, let $\mathcal{P}$ denote the set of prime numbers with digits restricted to $\mathcal{A}$, when written in base-$b$. We prove that if $A\subset \mathbb{N}$ has…

We establish several new probabilistic, dynamical, dimensional and number theoretical phenomena connected with Ostrogradsky-Sierpi\'nski-Pierce expansion. First of all, we develop metric, ergodic and dimensional theories of the…

The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…

Onsager's variational principle is generalized to address the diffusive dynamics of an electrolyte solution composed of charge-regulated macro-ions and counterions. The free energy entering the Rayleighian corresponds to the…

Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these…

We prove a law of large numbers for a class of multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of…

The Ising model in the presence of a random field, drawn from the asymmetric and anisotropic trimodal probability distribution $P(h_{i})=p\; \delta(h_{i}-h_{0}) + q \delta (h_{i}+ \lambda *h_{0}) + r \delta (h_{i})$, is investigated. The…

Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random…

Random walks of n steps taken into independent uniformly random directions in a d-dimensional Euclidean space (d larger than 1), are named Dirichlet when their step lengths are distributed according to a Dirichlet law. The latter continuous…

Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…

We study the long-time behavior of radially symmetric solutions to the Vlasov-Poisson equation consisting of an attractive point mass and a small, suitably localized and absolutely continuous distribution of particles: if the latter is…

This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…

We study the statistics of the force felt by a particle in the class of spatially correlated distribution of identical point-like particles, interacting via a $1/r^2$ pair force (i.e. gravitational or Coulomb), and obtained by randomly…