相关论文: Ergodic Considerations in the Gravitational Potent…
We introduce the concepts of Baire Ergodicity and Ergodic Formalism, employing them to study topological and statistical attractors. Specifically, we establish the existence and finiteness of such attractors and provide applications for…
This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The…
By performing a global magnetohydrodynamical (MHD) simulation for the Milky Way with an axisymmetric gravitational potential, we propose that spatially dependent amplification of magnetic fields possibly explains the observed noncircular…
Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile…
Near-future surveys promise a dramatic improvement in the number and precision of astrometric, photometric and spectroscopic measurements of stars in the Milky Way's disk. We examine the impact of such surveys on our understanding of the…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.
This paper investigates performance guarantees on coverage-based ergodic exploration methods in environments containing disturbances. Ergodic exploration methods generate trajectories for autonomous robots such that time spent in each area…
Necessary and sufficient conditions for a Markov chain to be ergodic are that the chain is irreducible and aperiodic. This result is manifest in the case of random walks on finite groups by a statement about the support of the driving…
We present a rigorous and practical way of constraining the Galactic potential based on the phase-space information for many individual stars. Such an approach is needed to dynamically model the data from ongoing spectroscopic surveys of…
In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…
The spatial distribution of galaxies we observed is subject to the given condition that we, human beings are sitting right in a galaxy -- the Milky Way. Thus the ergodicity assumption is questionable in interpretation of the observed galaxy…
We formulate a criterion for the existence and uniqueness of an invariant measure for a Markov process taking values in a Polish phase space. In addition, weak-$^*$ ergodicity, that is, the weak convergence of the ergodic averages of the…
We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for…
We use astrophysical data to shed light on fundamental physics by constraining parametrized theoretical cosmological and gravitational models. Gravitational parameters are those constants that parametrize possible departures from Einstein's…
This research addresses the challenge of executing multi-UAV survey missions over diverse terrains characterized by varying elevations. The approach integrates advanced two-dimensional ergodic search technique with model predictive control…
With theoretical constraints such as perturbative unitarity and vacuum stability conditions and updated experimental data of Higgs measurements and direct searches for exotic scalars at the LHC, we perform an updated scan of the allowed…
The recently suggested SEE (Satellite Energy Exchange) method of measuring the gravitational constant $G$, possible equivalence principle violation (measured by the E\"{o}tv\"{o}s parameter $\eta$) and the hypothetic 5th force parameters…
Solar System tests give nowadays constraints on the estimated value of the cosmological constant, which can be accurately derived from different experiments regarding gravitational redshift, light deflection, gravitational time-delay and…
In this fourth article on weighing the Galactic disk using the shape of the phase-space spiral, we have tested our method on a billion particle three-dimensional N-body simulation, comprised of a Milky Way like host galaxy and a merging…