Related papers: Slow relaxation dynamics and aging in random walks…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of…
Logarithmic aging phenomena are prevalent in various systems, including electronic materials and biological structures. This study utilizes a generalized continuous time random walk (CTRW) framework to investigate the mechanisms behind the…
We consider a one-dimensional simple random walk killed by quenched soft obstacles. The position of the obstacles is drawn according to a renewal process with a power-law increment distribution. In a previous work, we computed the…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…
We study the mechanism behind dynamical trappings experienced during Wang-Landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the…
Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this supplementary material for the paper "Navigability of interconnected networks…
In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are…
We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.
Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to…
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard…
We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular ($A/L \times L)$ landscape and, once reached, they…
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…
The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one, two and three dimensional contin- uum. In all cases, the…
Recently, random walks on dynamic graphs have been studied because of their adaptivity to the time-varying structure of real-world networks. In general, there is a tremendous gap between static and dynamic graph settings for the lazy simple…
The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…