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Fractal phenomena may be widely observed in a great number of complex systems. In this paper, we revisit the well-known Vicsek fractal, and study some of its structural properties for purpose of understanding how the underlying topology influences its dynamic behaviors. For instance, we analytically determine the exact solution to mean first-passage time for random walks on Vicsek fractal in a more light mapping-based manner than previous other methods, including typical spectral technique. More importantly, our method can be quite efficient to precisely calculate the solutions to mean first-passage time on all generaliz
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the firs
In this paper we study first-passge percolation models on Delaunay triangulations. We show a sufficient condition to ensure that the asymptotic value of the rescaled first-passage time, called the time constant, is strictly positive and derive some u
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, especially com
Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach consists in poi
We study the time constant $mu(e_{1})$ in first passage percolation on $mathbb Z^{d}$ as a function of the dimension. We prove that if the passage times have finite mean, $$lim_{d to infty} frac{mu(e_{1}) d}{log d} = frac{1}{2a},$$ where $a in [0,inf