Renewal theory with fat-tailed distributed sojourn times: Typical versus rare

@article{Wang2018RenewalTW,
  title={Renewal theory with fat-tailed distributed sojourn times: Typical versus rare},
  author={Wanli Wang and Johannes H. P. Schulz and Weihua Deng and Eli Barkai},
  journal={Physical Review E},
  year={2018}
}
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate function approach from large deviation theory does not hold and new tools must be considered. Here we investigate the large deviations of the number of renewals, the forward and backward recurrence time, the occupation time, and the time interval straddling… 
Occupation time of a renewal process coupled to a discrete Markov chain
. A semi-Markov process is one that changes states in accordance with a Markov chain but takes a random amount of time between changes. We consider the generalisation to semi-Markov processes of the
Microscopic dynamics in rare events: generalized L\'evy processes and the big jump principle
The prediction and estimate of rare events is an important task in disciplines that range from physics and biology, to economics and social science. A peculiar aspect of the mechanism that drives
Moses, Noah and Joseph effects in Lévy walks
We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the
Hitchhiker model for Laplace diffusion processes.
TLDR
This model explains how Laplace diffusion is controlled by size fluctuations of single molecules, independently of the diffusion law which they follow, and shows how single-molecule tracking and data analysis, in a many-body system, is highly nontrivial as tracking of a single particle or many in parallel yields vastly different estimates for the diffusivity.
Monitoring Lévy-process crossovers
Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion
Strong anomalous diffusion phenomena are often observed in complex physical and biological systems, which are characterized by the nonlinear spectrum of exponents $q\nu(q)$ by measuring the absolute
Monitoring L\'evy-Process Crossovers
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among
Ergodic properties of heterogeneous diffusion processes in a potential well.
TLDR
This work investigates the ergodic and nonergodic behavior of these processes in an arbitrary potential well U(x) in terms of the observable-occupation time for large-x behavior for long times in an overdamped Langevin equation with space-dependent diffusivity D(x).
Nonergodicity of d-dimensional generalized Lévy walks and their relation to other space-time coupled models.
We investigate the nonergodicity of the generalized Lévy walk introduced by Shlesinger et al. [Phys. Rev. Lett. 58, 1100 (1987)PRLTAO0031-900710.1103/PhysRevLett.58.1100] with respect to the squared
Dynamical glass in weakly nonintegrable Klein-Gordon chains.
TLDR
The dynamics of observables which become the conserved actions in the integrable limit are analyzed, and distributions of their finite time averages are computed to obtain the ergodization time scale T_{E} on which these distributions converge to δ distributions.
...
1
2
3
...

References

SHOWING 1-10 OF 103 REFERENCES
Renewal Theory for a System with Internal States
We investigate a stochastic signal described by a renewal process for a system with N states. Each state has an associated joint distribution for the signal’s intensity and its holding time. We
Aging renewal theory and application to random walks
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random
Statistics of the Occupation Time of Renewal Processes
We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the
Characteristic Sign Renewals of Kardar–Parisi–Zhang Fluctuations
Tracking the sign of fluctuations governed by the $$(1+1)$$(1+1)-dimensional Kardar–Parisi–Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an
Distributional behaviors of time-averaged observables in the Langevin equation with fluctuating diffusivity: Normal diffusion but anomalous fluctuations.
TLDR
It is found that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.
Infinite densities for Lévy walks.
TLDR
This paper finds a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α, and the diffusion coefficient K(α).
Large Fluctuations for Spatial Diffusion of Cold Atoms.
TLDR
This work uses a new approach to study the large fluctuations of a heavy-tailed system, where the standard large-deviations principle does not apply, and derives general relations which extend the theory to a class of systems with multifractal moments.
Fluctuations around equilibrium laws in ergodic continuous-time random walks.
TLDR
While the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations, which is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.
Aging is a log-Poisson process, not a renewal process.
TLDR
A physically motivated description of the log-Poisson process characteristic of the intermittent and decelerating dynamics of jammed matter usually activated by record-breaking fluctuations ("quakes") is proposed and shown to provide a universal model for aging.
Statistics of the longest interval in renewal processes
TLDR
It is shown that the fluctuations of $\ell^\alpha_{\max}(t)/t$ are governed, in the large $t$ limit, by a stationary universal distribution which depends on both $\theta$ and $\alpha$, which is computed exactly.
...
1
2
3
4
5
...