Related papers: Record Statistics of Continuous Time Random Walk
Permutation entropy has become a standard tool for time series analysis that exploits the temporal properties of these data sets. Many current applications use an approach based on Shannon entropy, which implicitly assumes an underlying…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
We revisit the statistics of extremes and records of symmetric random walks with stochastic resetting, extending earlier studies in several directions. We put forward a diffusive scaling regime (symmetric step length distribution with…
We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of $t$-periodic walks and its mean, when the cardinality of the…
The interaction between individuals in biological populations, dilute components of chemical systems, or particles transported by turbulent flows depends critically on their contact statistics. This work clarifies those statistics under the…
We study survival time statistics in a noisy sample space reducing (SSR) process. Our simulations suggest that both the mean and standard deviation scale as $\sim N/N^{\lambda}$, where $N$ is the system size and $\lambda$ is a tunable…
We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points,…
We study a simple run-and-tumble random walk whose switching frequency from run mode to tumble mode and the reverse depend on a stochastic signal. We consider a particularly sharp, step-like dependence, where the run to tumble switching…
We apply the formalism of the continuous time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
The range, local times, and periodicity of symmetric, weakly asymmetric and asymmetric random walks at the time of exit from a strip with $N$ locations are considered. Several results on asymptotic distributions are obtained.
Functional limit theorem for continuous-time random walks (CTRW) are found in general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional…
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
We analyze record-breaking events in time series of continuous random variables that are subsequently discretized by rounding down to integer multiples of a discretization scale $\Delta>0$. Rounding leads to ties of an existing record,…
We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal…
While the fat tailed jump size and the waiting time distributions characterizing individual human trajectories strongly suggest the relevance of the continuous time random walk (CTRW) models of human mobility, no one seriously believes that…