Hitting and Trapping Times on Branched Structures

Abstract

In this work we consider a simple random walk embedded in a generic branched structure and we find a close-form formula to calculate the hitting time $H\left(i,f\right)$ between two arbitrary nodes $i$ and $j$. We then use this formula to obtain the set of hitting times $\left\{H\left(i,f\right)\right\}$ for combs and their expectation values, namely the mean-first passage time $\left( \mbox{MFPT}_{f} \right)$, where the average is performed over the initial node while the final node $f$ is given, and the global mean-first passage time $\left( \mbox{GMFPT} \right)$, where the average is performed over both the initial and the final node. Finally, we discuss applications in the context of reaction-diffusion problems.

11 pages, 14 figures

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• The two-particle problem in comb-like structures
• Exact results for the first-passage properties in a class of fractal networks
• Mesoscopic description of random walks on combs
• Interplay between particle trapping and heterogeneity in anomalous diffusion
• Dynamics of "comb-of-comb" networks
• Volatilities analysis of first-passage time and first-return time on a small-world scale-free network
• Dynamics of soft interacting particles on a comb