Related papers: When Euler met Brun
We study random surfaces constructed by glueing together $N/k$ filled $k$-gons along their edges, with all $(N-1)!! = (N-1)(N-3)...3\cdot 1$ pairings of the edges being equally likely. (We assume that lcm $\{2,k\}$ divides $N$.) The Euler…
In this paper we derive weak limits for the discretization errors of sampling barrier-hitting and extreme events of Brownian motion by using the Euler discretization simulation method. Specifically, we consider the Euler discretization…
We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…
95 years ago Hoheisel proved the existence of primes in the sub-linear interval \[ \left[x, x+x^{1-{1\over 33000}}\right] \qquad \hbox{for $x$ sufficiently large}. \] This was improved by Heilbronn, proving existence of primes in the…
Let pi(x) denote the number of primes smaller or equal to x. We compare sqrt{pi}(x) with sqrt{R}(x) and sqrt{li}(x), where R(x) and li(x) are the Riemann function and the logarithmic integral, respectively. We show a regularity in the…
We prove that there are infinitely often pairs of primes much closer than the average spacing between primes - almost within the square root of the average spacing. We actually prove a more general result concerning the set of values taken…
The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with…
We investigate a recursively generated sequence of random variables that begins with an Exponential random variable with parameter (i.e., inverse-mean) 1, and continues with additional Exponentials, each of whose random parameter possesses…
Starting with the Brezis-Browder principle, we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature. Relationships among the elements of different sets of assumptions are…
By establishing an improved level of distribution we study almost primes of the form $f(p,n)$ where $f$ is an irreducible binary form over $\mathbb Z$.
We bring to bear an empirical model of the distribution of twin primes and produce two distinct results. The first is that we can make a quantitative probabilistic prediction of the occurrence of gaps in the sequence of twins within the…
We study the Euler-Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this…
We survey some past conditional results on the distribution of large differences between consecutive primes and examine how the Hardy-Littlewood prime k-tuples conjecture can be applied to this question.
Strong encounters between single stars and binaries play a pivotal role in the evolution of star clusters. Such encounters can also dramatically modify the orbital parameters of binaries, exchange partners in and out of binaries, and are a…
We show interaction between high- and low-frequency modes in periodic $\alpha$-FPU chains with alternating large masses. The treatment discusses the difficult case where the number of particles $N=2p$ involves $p$ prime. A key role is…
Let $K$ be a finite Galois extension of $\mathbb{Q}$. We count primes in short intervals represented by the norm of a prime ideal of $K$ satisfying a small sector condition determined by Hecke characters. We also show that such primes are…
Let $(X,Y)\in\mathcal{X}\times \mathcal{Y}$ be a random couple with unknown distribution $P$. Let $\GG$ be a class of measurable functions and $\ell$ a loss function. The problem of statistical learning deals with the estimation of the…
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…
Intracellular processes often rely on the timely encounter of mobile reaction partners, including intermittently motor-driven organelles. The underlying cytoskeletal network presents a complex landscape that both directs particle movement…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…