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We study random walks on a family of treelike regular fractals with a trapfixed on a central node. We obtain all the eigenvalues and their correspondingmultiplicities for the associated stochastic master equation, with theeigenvalues being provided through an explicit recursive relation. We alsoevaluate the smallest eigenvalue and show that its reciprocal is approximatelyequal to the mean trapping time. We expect that our technique can also beadapted to other regular fractals with treelike structures.

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