Related papers: Meeting time distributions in Bernoulli systems

We present here the first observationally based determination of the rate of occurrence of circumbinary planets. This is derived from the publicly available Kepler data, using an automated search algorithm and debiasing process to produce…

The {\it Kepler} mission has detected thousands of planetary systems with 1-7 transiting planets packed within 0.7~au from their host stars. There is an apparent excess of single-transit planet systems that cannot be explained by transit…

We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius $R$ and taking the limit as $R \to \infty$. These relations take the form of mass…

Multi-planetary systems detected by the Kepler mission present an excess of planets close to first-order mean-motion resonances (2:1 and 3:2) but with a period ratio slightly higher than the resonant value. Several mechanisms have been…

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the…

The questions of how planets form and how common Earth-like planets are can be addressed by measuring the distribution of exoplanet masses and orbital periods. We report the occurrence rate of close-in planets (with orbital periods less…

We present a Monte Carlo model for the structure of low mass (total mass < 25 earth mass) planetary systems that form by the in situ gravitational assembly of planetary embryos into final planets. Our model includes distributions of mass,…

This article rigorously analyzes the meeting time between pursuers and evaders performing random walks on digraphs. There exist several bounds on the expected meeting time between random walkers on graphs in the literature, however,…

We present some measurements and ideas for response time statistics in ERP systems. It is shown that the response time distribution of a given transaction in a given system is generically a log-normal distribution or, in some situations, a…

We develop an analytic model for transit timing variations produced by orbital conjunctions between gravitationally interacting planets. If the planetary orbits have tight orbital spacing, which is a common case among the Kepler planets,…

Bernoulli sieve is a recursive construction of a random composition (ordered partition) of integer $n$. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of component…

In electron transport, the tunnelling time is the time taken for an electron to tunnel out of a system after it has tunnelled in. We define the tunnelling time distribution for quantum processes in a dissipative environment and develop a…

We consider a particle diffusing outside a compact planar set and investigate its boundary local time $\ell_t$, i.e., the rescaled number of encounters between the particle and the boundary up to time $t$. In the case of a disk, this is…

The {\it Kepler} mission revealed a population of compact multiple-planet systems with orbital periods shorter than a year, and occasionally even shorter than a day. By analyzing a sample of 102 {\it Kepler} and {\it K2} multi-planet…

Given a topologically transitive system on the unit interval, one can investigate the cover time, i.e. time for an orbit to reach certain level of resolution in the repeller. We introduce a new notion of dimension, namely the stretched…

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse…

Do sub-Neptunes assemble close to where we see them or do they form full-fledged farther away from their host star then migrate inwards? We explore this question using the distribution of measured orbital periods, one of the most…

The setting for this brief paper is R^3. Distance between two spheres is understood as distance delta between spherical centers. For instance, a Reuleaux tetrahedron T is the intersection of four unit balls satisfying delta=1 pairwise.…

We examine the convergence of ergodic averages along polynomials in Toeplitz systems and prove that it is possible for averages along one polynomial to converge, and along another to diverge. We also study density of the polynomial orbits…

This paper considers whether the population of known transiting exoplanets provides evidence for additional outer planets on inclined orbits, due to the perturbing effect of such planets on the orbits of inner planets. As such, we develop a…