相关论文: Ergodic Considerations in the Gravitational Potent…
We show that a small, but \textit{measurable} shift in the eclipse mid-point time of eclipsing binary (EBs) stars of $\sim$ 0.1 seconds over a decade baseline can be used to directly measure the Galactic acceleration of stars in the Milky…
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…
Observational data from the ESA astrometric mission Gaia determining the positions of celestial objects within an accuracy of few microarcseconds will be soon fully available. Other satellite-based space missions are currently planned to…
Several satellite missions, devoted to the study of the Earth gravity field, have been launched (like CHAMP, recently). This year, GRACE (Gravity Recovery and Climate Experiment) will allow us to obtain a more precise geoid. But the most…
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie, Harris, & Widrow (2015) and Eadie &…
We introduce the emPDF (Empirical Distribution Function), a novel dynamical modeling method that infers the gravitational potential from kinematic tracers with optimal statistical efficiency under the minimal assumption of steady state.…
The parameters of an axisymmetric model for the gravitational potential of the Galaxy have been refined. The basic curve of the Galaxy's rotation in a distance interval of $R:0-190$ kpc was constructed using the velocities of masers,…
Here we present an ergodic theorem which adapts a Theorem by J. Elton to the classical thermodynamical formalism and to ergodic transport. First, we discuss how Elton's theorem can be used to characterise Gibbs measures for expanding maps.…
The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural…
A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increase, and the final state is characterized by a distribution…
Although a number of solutions exist for the problems of coverage, search and target localization---commonly addressed separately---whether there exists a unified strategy that addresses these objectives in a coherent manner without being…
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both position-independent and position-dependent…
The motion of the baryonic components of the Milky Way is governed by both luminous and dark matter content of the Galaxy. Thus, the dynamics of the Milky Way globular clusters can be used as tracers to infer the mass model of the Galaxy up…
We consider a Metropolis--Hastings method with proposal $\mathcal{N}(x, hG(x)^{-1})$, where $x$ is the current state, and study its ergodicity properties. We show that suitable choices of $G(x)$ can change these compared to the Random Walk…
Using the method that was developed in the first paper of this series, we measure the vertical gravitational potential of the Galactic disk from the time-varying structure of the phase-space spiral, using data from Gaia as well as…
Tetrahedral configurations of spacecraft on unperturbed heliocentric orbits allow for highly precise observations of small spatial changes in the gravitational field, especially those affecting the gravity gradient tensor (GGT). The…
A metric-field approach to gravitation is presented. It is based on an idea of dependency of space-time properties on measuring instruments. Some bimetric equations that realize this idea are considered. They were tested by the binary…
We perform a test of John Moffat's Modified Gravity theory (MOG) within the Milky Way, adopting the well known "Rotation Curve" method. We use the dynamics of observed tracers within the disk to determine the gravitational potential as a…
Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in…
Ergodic optimization is the study of problems relating to maximizing orbits, maximizing invariant measures and maximum ergodic averages. An orbit of a dynamical system is called f-maximizing if the time average of the real-valued function f…