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

References in corpus (5)

• First-passage times in complex scale-invariant media
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Exact mean first-passage time on the T-graph
• Ring structures and mean first passage time in networks
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Cited by in corpus (2)

• Exact calculations of first-passage properties on the pseudofractal scale-free web
• Exact results for the first-passage properties in a class of fractal networks