Related papers: Flux fluctuations in a multi-random-walker model a…
Kinetically grown self-avoiding walks on various types of generalized random networks have been studied. Networks with short- and long-tailed degree distributions $P(k)$ were considered ($k$, degree or connectivity), including scale-free…
The Continuous Time Random Walk (CTRW) formalism is used to model the non-Poisson relaxation of a system response to perturbation. Two mechanisms to perturb the system are analyzed: a first in which the perturbation, seen as a potential…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…
We consider a discrete-time random walk on a one-dimensional lattice with space and time-dependent random jump probabilities, known as the Beta random walk. We are interested in the probability that, for a given realization of the jump…
Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the $1/\sqrt{t}$…
We suggest a model for data losses in a single node of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. The model shows critical behavior with an abrupt…
We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important…
We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…
The behavior of a spin undergoing Larmor precession in the presence of fluctuating fields is of interest to workers in many fields. The fluctuating fields cause frequency shifts and relaxation which are related to their power spectrum,…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We study the Tree Builder Random Walk: a randomly growing tree, built by a walker as she is walking around the tree. Namely, at each time $n$, she adds a leaf to her current vertex with probability $p_n \asymp n^{-\gamma}$, $\gamma\in…
Using numerical simulations and scaling theory we study the dynamics of the world-wide Web from the growth rules recently proposed in Ref. [1] with appropriate parameters. We demonstrate that the emergence of power-law behavior of the out-…
We study pattern formation, fluctuations and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy consuming proteins embedded in the plasma…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
We consider the thermodynamic behavior of local fluctuations occurring in a stable or metastable bulk phase. For a system with three or more phases, a simple analysis based on classical nucleation theory predicts that small fluctuations…
We theoretically investigate the effect of random fluctuations on the motion of elongated microswimmers near hydrodynamic transport barriers in externally-driven fluid flows. Focusing on the two-dimensional hyperbolic flow, we consider the…