Complete spectrum of stochastic master equation for random walks on treelike fractals

Abstract

We study random walks on a family of treelike regular fractals with a trap fixed on a central node. We obtain all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation, with the eigenvalues being provided through an explicit recursive relation. We also evaluate the smallest eigenvalue and show that its reciprocal is approximately equal to the mean trapping time. We expect that our technique can also be adapted to other regular fractals with treelike structures.

Definitive version accepted for publication in EPL (Europhysics Letters)

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• Optimal and suboptimal networks for efficient navigation measured by mean-first passage time of random walks
• Mean first-passage time for random walks in general graphs with a deep trap
• Controlling the efficiency of trapping in treelike fractals
• Spectrum of the tight-binding model on Cayley Trees and comparison with Bethe Lattices
• Random walks in unweighted and weighted modular scale-free networks with a perfect trap
• Optimal scale-free network with a minimum scaling of transport efficiency for random walks with a perfect trap
• Anomalous behavior of trapping in extended dendrimers with a perfect trap