Related papers: Point estimates, Simpson's paradox and nonergodici…
The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by…
We investigate the well-posedness and long-time behavior of a general continuum neural field model with Gaussian noise on possibly unbounded domains. In particular, we give conditions for the existence of invariant probability measures by…
The study of citations in the scientific literature crosses the boundaries between the traditional branches of science and stands on its own as a most profitable research field dubbed the `science of science'. Although the understanding of…
Meta-analysis is an important tool for combining results from multiple studies and has been widely used in evidence-based medicine for several decades. This paper reports, for the first time, an interesting and valuable paradox in…
It is of great current interest to establish toy models of ergodicity breaking transitions in quantum many-body systems. Here we study a model that is expected to exhibit an ergodic to nonergodic transition in the thermodynamic limit upon…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
In this paper, we consider subgeometric (specifically, polynomial) ergodicity of univariate nonlinear autoregressions with autoregressive conditional heteroskedasticity (ARCH). The notion of subgeometric ergodicity was introduced in the…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
Biomolecular force fields have been traditionally derived based on a mixture of reference quantum chemistry data and experimental information obtained on small fragments. However, the possibility to run extensive molecular dynamics…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…
We consider skew-products with concave interval fiber maps over a certain subshift obtained as the projection of orbits staying in a given region. It generates a new type of (essentially) coded shift. The fiber maps have expanding and…
There are three principle paradigms of statistics: Bayesian, frequentist and information-based inference. Although these paradigms are in agreement in some contexts, the Lindley paradox describes a class of problems, models of unknown…
The study of human mobility patterns is a crucially important research field for its impact on several socio-economic aspects and, in particular, the measure of regularity patters of human mobility can provide a across-the-board view of…
All scientific interpretations of statistical outputs depend on background (auxiliary) assumptions that are rarely delineated or explicitly interrogated. These include not only the usual modeling assumptions, but also deeper assumptions…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a…
For dynamical systems satisfying the approximate $\mathbb{Z}^{d}$ or $\mathbb{Z}_+^{d}$-product property and asymptotically entropy expansiveness, we establish a precise description of the structure of their space of invariant measures. In…
Ergodicity economics is a new branch of economic theory that notes the conceptual difference between time averages and expectation values, which coincide only for ergodic observables. It postulates that individual agents maximise the time…
Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…