Related papers: Ergodicity Breaking and Localization
Heterogeneous diffusion processes are prevalent in various fields, including the motion of proteins in living cells, the migratory movement of birds and mammals, and finance. These processes are often characterized by time-varying dynamics,…
Fractional extensions of the cable equation have been proposed in the literature to describe transmembrane potential in spiny dendrites. The anomalous behavior has been related in the literature to the geometrical properties of the system,…
We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution for any continuous, differentiable…
Random walks are a fundamental tool for analyzing realistic complex networked systems and implementing randomized algorithms to solve diverse problems such as searching and sampling. For many real applications, their actual effect and…
The edge-reinforced random walk (ERRW) is a random process on the vertices of a graph that is more likely to cross the edges it has visited in the past. Depending on the strength of the reinforcement, the ERRW of a single particle can…
Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…
Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a…
We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the…
The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk…
We present an exact solution for the probability density function $P(\tau=t_{\min}-t_{\max}|T)$ of the time-difference between the minimum and the maximum of a one-dimensional Brownian motion of duration $T$. We then generalise our results…
We show that the longitudinal position $x(t)$ of a particle in a $(d+1)$-dimensional layered random velocity field (the Matheron-de Marsily model) can be identified as a fractional Brownian motion (fBm) characterized by a variable Hurst…
Characterizing hydrodynamic transport in fractured rocks is essential for carbon storage and geothermal energy production. Multiscale heterogeneities lead to anomalous solute transport, with breakthrough-curve (BTC) tailing and nonlinear…
For $0<\alpha \leq 2$ and $0<H<1$, an $\alpha$-time fractional Brownian motion is an iterated process $Z = \{Z(t)=W(Y(t)), t \ge 0\}$ obtained by taking a fractional Brownian motion $\{W(t), t\in \RR{R} \}$ with Hurst index $0<H<1$ and…
We investigate the dynamics of a run-and-tumble particle in a double-well potential and demonstrate that, in stark contrast to Brownian particles, active dynamics can lead to strong ergodicity breaking. When the barrier height exceeds a…
In this work, we consider a modification of time \emph{inhomogeneous} branching random walk, where the driving increment distribution changes over time macroscopically. Following Bandyopadhyay and Ghosh (2021), we give certain independent…
Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter $H \in (0, 1)$ called the Hurst index. The use of time-changed processes in modeling often requires the…
Complex systems display anomalous diffusion, whose signature is a space/time scaling $x\sim t^\delta$ with $\delta \ne 1/2$ in the Probability Density Function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g.,…
We show that when Brownian motion takes place in a heterogeneous medium, the presence of local forces and transport coefficients leads to deviations from a Gaussian probability distribution that make that the ratio between forward and…
A multifractal random walk (MRW) is defined by a Brownian motion subordinated by a class of continuous multifractal random measures $M[0,t], 0\le t\le1$. In this paper we obtain an extension of this process, referred to as multifractal…
Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory seen in space physics and elsewhere. Natural time series frequently combine both effects, and Linear Fractional Stable…