Related papers: Navigation by anomalous random walks on complex ne…
Community detection is of fundamental significance for understanding the topology characters and the spreading dynamics on complex networks. While random walk is widely used and is proven effective in many community detection algorithms,…
We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial…
Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics.…
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…
A global picture of a random particle movement is given by the convex hull of the visited points. We obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes…
In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks. We present a general approach to analyzing these strategies by defining the dynamics as a discrete-time Markovian…
Search strategies based on random walk processes with long-tailed jump length distributions (Levy walks) on the one hand and intermittent behavior switching between local search and ballistic relocation phases on the other, have been…
Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We…
The first-passage time (FPT) is the time it takes a system variable to cross a given boundary for the first time. In the context of Markov networks, the FPT is the time a random walker takes to reach a particular node (target) by hopping…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…
The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on a hyper-cubic lattice and study ordering probabilities associated with these…
Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take…
We show that Lagrangian measurements in active turbulence bear imprints of turbulent and anomalous streaky hydrodynamics leading to a self-selection of persistent trajectories - Levy walks - over diffusive ones. This emergent dynamical…
We present a heuristic derivation of the first passage time exponent for the integral of a random walk [Y. G. Sinai, Theor. Math. Phys. {\bf 90}, 219 (1992)]. Building on this derivation, we construct an estimation scheme to understand the…
We investigate network exploration by random walks defined via stationary and adaptive transition probabilities on large graphs. We derive an exact formula valid for arbitrary graphs and arbitrary walks with stationary transition…