Related papers: Random walks on bifractal networks
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…
This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic…
We present a Monte Carlo study of the fractal geometry of clusters formed by discrete-time simple random walks (sRW) of $L^2$ steps on a periodic square $L\times L$ lattice. We verify with high precision that the asymptotic behavior of the…
We investigate the dynamic scaling properties of stochastic particle systems on a non-deterministic scale-free network. It has been known that the dynamic scaling behavior depends on the degree distribution exponent of the underlying…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Fractals are fascinating structures, not only for their aesthetic appeal, but also because they allow for the investigation of physical properties in non-integer dimensions. In these unconventional systems, a myriad of intrinsic features…
In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce…
We analyze the differences between the horizontal and the vertical component of the simple random walk on the 2-dimensional comb. In particular we evaluate by combinatorial methods the asymptotic behaviour of the expected value of the…
We propose a general model of unweighted and undirected networks having the scale-free property and fractal nature. Unlike the existing models of fractal scale-free networks (FSFNs), the present model can systematically and widely change…
The explicit determinations of the mean first-passage time (MFPT) for trapping problem are limited to some simple structure, e.g., regular lattices and regular geometrical fractals, and determining MFPT for random walks on other media,…
It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in…
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…
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 consider random walks on comb- and brush-like graphs consisting of a base (of fractal dimension $D$) decorated with attached side-groups. The graphs are also characterized by the fractal dimension $D_a$ of a set of anchor points where…
The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form…
We investigate the multifractals of the normalized first passage time on one-dimensional small-world network with both reflecting and absorbing barriers. The multifractals is estimated from the distribution of the normalized first passage…
We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in…
The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are…
We demonstrate analytically and numerically the possibility that the fractal property of a scale-free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure. It is found that the mass…
We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the…