Related papers: The Buffon needle problem for L\'evy distributed s…
We describe a previously unexplored effect of the continuous spontaneous localization model whereby a correlation develops in the distributions of two nearby non-interacting particles following a period of diffusion. We propose the use of…
Some of the parameters we call ``constants of Nature'' may in fact be variables related to the local values of some dynamical fields. During inflation, these variables are randomized by quantum fluctuations. In cases when the variable in…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
The hypothesis that high dimensional data tend to lie in the vicinity of a low dimensional manifold is the basis of manifold learning. The goal of this paper is to develop an algorithm (with accompanying complexity guarantees) for fitting a…
In a general simulation of random walking (with the angle of motion picked uniformly), it can be seen that the probability of crossing a WiFi TX-RX link is directly proportional to the per-step distance and inversely proportional to the…
We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of…
We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the $1/\sqrt{t}$…
Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to…
Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance. Advocates of "emergence" view these capabilities as unlocked at a specific scale, but others attribute…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
The scan statistic is by far the most popular method for anomaly detection, being popular in syndromic surveillance, signal and image processing, and target detection based on sensor networks, among other applications. The use of the scan…
We consider a natural model of random knotting- choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to…
The scattering of a weakly bound (halo) projectile nucleus by a heavy target nucleus is investigated. A new approach, called the Uncorrelated Scattering Approximation, is proposed. The main approximation involved is to neglect the…
Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and…
It is our intention to provide via fractional calculus a generalization of the pure and compound Poisson processes, which are known to play a fundamental role in renewal theory, without and with reward, respectively. We first recall the…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
We study statistics of tiles in random incommensurable Kakutani sequences of partitions in $\mathbb{R}^d$. We provide explicit formulas that illustrate the dependence on the combinatorial structure, the volumes of the participating tiles…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…