Related papers: Lonely runners in function fields
Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with an alternating aerial and…
Reflected random walk in higher dimension arises from an ordinary random walk (sum of i.i.d. random variables): whenever one of the reflecting coordinates becomes negative, its sign is changed, and the process continues from that modified…
In Einstein's Special Theory of Relativity, all observers measure the speed of light, $c$, to be the same. However, this refers to the round trip speed, where a clock at the origin times the outward and return trip of light reflecting off a…
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are…
We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…
We use character sums to confirm several recent conjectures of V. I. Arnold on the uniformity of distribution properties of a certain dynamical system in a finite field. On the other hand, we show that some conjectures are wrong. We also…
This paper investigates the difference between the circular and elliptical cases in one-on-one pursuit and evasion problems. Using the simultaneous differential equation derived by Barton and Eliezer, we derive a dynamical system based on…
Tracking physical activity reliably is becoming central to many research efforts. In the last years specialized hardware has been proposed to measure movement. However, asking study participants to carry additional devices has drawbacks. We…
Discrete pedestrian simulation models are viable alternatives to particle based approaches based on a continuous spatial representation. The effects of discretisation, however, also imply some difficulties in modelling certain phenomena…
The Polya number of a classical random walk on a regular lattice is known to depend solely on the dimension of the lattice. For one and two dimensions it equals one, meaning unit probability to return to the origin. This result is extremely…
Performance measures such as stride length in athletics and the pace of runners can be estimated using different tricks such as measuring the number of steps divided by the running length or helping with markers printed on the track.…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
Using standard quantum field theory, we discuss several theoretical aspects of the possible running of the cosmological constant (CC) term in Einstein's equations. The basic motivation for the present work is to emphasize that this…
In this paper we deal analytically with a version of the so called clock paradox in which the moving clock performs a circular motion of constant radius. The rest clock is denoted as (1), the rotating clock is (2), the inertial frame in…
We derive a simple consistency relation from the running of the tensor-to-scalar ratio. This new relation is first order in the slow-roll approximation. While for single field models we can obtain what can be found by using other…
Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. We adopt here this concept for single-particle random walks and demonstrate that the corresponding…
The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the…
Henze and Malikiosis (2017) have shown that the Lonely Runner Conjecture (LRC) can be restated as a convex-geometric question on the so-called LR zonotopes, lattice zonotopes with one more generator than their dimension. This relation…
This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and…
The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the 1D lattice random walk in discrete time. We determine the survival probability of the random walker in…