相关论文: Ergodicity recovery of random walk in heterogeneou…

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…

We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker,…

The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at modeling high dimensional data and nonlinear dynamics in…

Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C.D. Ferguson, W. Klein, and J.B. Rundle, Phys. Rev. E 60, 1359 (1999);…

The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…

Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…

We investigate continuous time random walks with truncated $\alpha$-stable trapping times. We prove distributional ergodicity for a class of observables; namely, the time-averaged observables follow the probability density function called…

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…

In this work the diffusion in the quenched trap model with diverging mean waiting times is examined. The approach of randomly stopped time is extensively applied in order to obtain asymptotically exact representation of the disorder…

Understanding the stochastic properties of conductance fluctuations in disordered mesoscopic systems is fundamental to quantum transport. In this work, we investigate the multifractal and ergodic properties of the fictitious time series of…

We present here for the first time a unifying perspective for the lack of equipartition in non-linear ordered systems and the low temperature phase-space fragmentation in disordered systems. We demonstrate that they are just two…

We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…

An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…

Ergodicity breaking is a challenge for biological and psychological sciences. Ergodicity is a necessary condition for linear causal modeling. Long-range correlations and non-Gaussianity characterizing various biological and psychological…

The central limit theorem for Markov chains generated by iterated function systems consisting of orientation preserving homeomorphisms of the interval is proved. We study also ergodicity of such systems.

We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence $D(x)\sim|x|^{\alpha}$ of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on…

The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far from equilibrium. Far from equilibrium, nonergodicity reigns. Nonergodicity implies that the average outcome for…

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…

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.…