Related papers: Discrete- and continuous-time random walks in 1D L…
A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We…
The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of…
We consider a minimal model of persistent random searcher with short range memory. We calculate exactly for such searcher the mean first-passage time to a target in a bounded domain and find that it admits a non trivial minimum as function…
This article considers the statistical properties of L\'evy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply.…
We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous…
Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…
The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
Almost all the media the particles move in are non-static. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement of the media, sometimes the non-static behaviours of the media can not be ignored.…
L\'{e}vy walk is a popular and more `physical' model to describe the phenomena of superdiffusion, because of its finite velocity. The movements of particles are under the influences of external potentials almost at anytime and anywhere. In…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective medium approximation (EMA) to find the disorder averaged (coarse-grained) dynamics. The EMA procedure…
Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the…
Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for…
We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
The standard Levy walk is performed by a particle that moves ballistically between randomly occurring collisions, when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events…
We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as L\'evy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…