Related papers: Joint ergodicity - 40 years on
In this paper, we study the regularity of the ergodic constants for the viscous Hamilton--Jacobi equations. We also estimate the convergent rate of the ergodic constant in the vanishing viscosity process.
We establish convergence in norm and pointwise almost everywhere for the non-conventional (in the sense of Furstenberg) bilinear polynomial ergodic averages \[ A_N(f,g)(x) := \frac{1}{N} \sum_{n =1}^N f(T^nx) g(T^{P(n)}x)\] as $N \to…
Weakly nonintegrable many-body systems can restore ergodicity in distinctive ways depending on the range of the interaction network in action space. Action resonances seed chaotic dynamics into the networks. Long range networks provide well…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
We study double averages along orbits for measure preserving actions of $\mathbb{A}^\omega$, the direct sum of countably many copies of a finite abelian group $\mathbb{A}$. In this article we show an $L^p$ norm-variation estimate for these…
This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances…
In this study, utilizing a specific exponential weighting function, we investigate the uniform exponential convergence of weighted Birkhoff averages along decaying waves and delve into several related variants. A key distinction from…
The almost sure convergence of ergodic averages in Birkhoff's pointwise ergodic theorem is known to fail in the finitely additive setting. We introduce a natural reformulation of almost sure convergence suitable for finitely additive…
We study optimization problems in ergodic theory from the view point of minimax problems. We give minimax characterizations of maximum ergodic averages involving time averages. Our approach works for the abstract variational principle of…
We prove essentially optimal $L^p(\mathbb{R})$-estimates for variational variants of the maximal Fourier multiplier operators considered by Bourgain in his work on pointwise convergence of polynomial ergodic averages. As a corollary of our…
In the physics literature "ergodicity" is taken to mean that a system, including a macroscopic one, visits all microscopic states in a relatively short time. We show that this is an impossibility even if that time is billions of years. We…
Any reliable biomarker has to be specific, generalizable, and reproducible across individuals and contexts. The exact values of such a biomarker must represent similar health states in different individuals and at different times within the…
In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric $\alpha$-stable processes. For this purpose, explicit and sharp criteria for…
We propose a random adaptation variant of time-varying distributed averaging dynamics in discrete time. We show that this leads to novel interpretations of fundamental concepts in distributed averaging, opinion dynamics, and distributed…
In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian Mean Field model and show that the life-time of…
Addressing global societal challenges necessitates insights and expertise that transcend the boundaries of individual disciplines. In recent decades, interdisciplinary collaboration has been recognised as a vital driver of innovation and…
We establish pointwise convergence for nonconventional ergodic averages taken along $\lfloor p^c\rfloor$, where $p$ is a prime number and $c\in(1,4/3)$ on $L^r$, $r\in(1,\infty)$. In fact, we consider averages along more general sequences…
The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains…
In this contribution we consider Collective Behaviours as coherent sequences of spatial configurations adopted by interacting agents through corresponding different structures over time. Multiple structures over time and their sequences are…