Related papers: Benford behavior resulting from stick and box frag…

We investigate fragmentation processes with a steady input of fragments. We find that the size distribution approaches a stationary form which exhibits a power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic behavior…

A necessary and sufficient condition ("nonresonance") is established for every solution of an autonomous linear difference equation, or more generally for every sequence $(x^\top A^n y)$ with $x,y\in \mathbb{R}^d$ and $A\in…

We prove Bombieri-Vinogradov type theorems for primes with a missing digit in their $b$-adic expansion for some large positive integer $b$. The proof is based on the circle method, which relies on the Fourier structure of the integers with…

This paper explores a real-world fundamental theme under a data science perspective. It specifically discusses whether fraud or manipulation can be observed in and from municipality income tax size distributions, through their aggregation…

Consider a quadratic polynomial $f\left(\xi_{1},\dots,\xi_{n}\right)$ of independent Bernoulli random variables. What can be said about the concentration of $f$ on any single value? This generalises the classical Littlewood--Offord problem,…

Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…

We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…

Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…

We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the $k$-divisor functions, where $k \neq 10^j$, and Hecke eigenvalues of newforms, such as Ramanujan tau…

The surface exponents, the scaling behavior and the bulk porosity of a generalized ballistic deposition (GBD) model are studied. In nature, there exist particles with varying degrees of stickiness ranging from completely non-sticky to fully…

Diversification is usually viewed as a reliable way to reduce risk, yet it can dramatically fail for heavy-tailed losses with infinite mean: pooling independent losses of this type may increase tail risk at every threshold. We study this…

We show that for most choices of an initial seed $x_0$, the sequence of the first $N$ iterates of $x_0$ under the $3x+1$ map approximately satisfies Benford's law.

An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable Lennard-Jones-type potential. We study two aspects of this problem. We start by…

We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…

Particles whose shapes couple translation to rotation display a rich array of behaviors as they sediment at low Reynolds number. We introduce a unifying perspective in which the possible dynamical regimes and bifurcations between them can…

We first study a $d$-dimensional branching Brownian motion (BBM) among mild Poissonian obstacles, where a random trap field in $\mathbb{R}^d$ is created via a Poisson point process. The trap field consists of balls of fixed radius centered…

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…

Many real-world networks exhibit the so-called small-world phenomenon: their typical distances are much smaller than their sizes. One mathematical model for this phenomenon is a long-range percolation graph on a $d$-dimensional box $\{0, 1,…

Let $b \ge 2$ be an integer. Not much is known on the representation in base $b$ of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which…