Recurrence of the frog model on the 3,2-alternating tree

Josh Rosenberg

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arXiv · 1701.02813

Recurrence of the frog model on the 3,2-alternating tree

Josh Rosenberg

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Abstract

Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is activated at that node, and begins its own random walk. The model described belongs to a class of problems that are collectively referred to as the frog model. Building on a recent proof of recurrence (meaning infinitely many frogs hit the root with probability one) on the regular binary tree, this paper establishes recurrence for the 3,2-alternating case.

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Josh Rosenberg. 2017-01-10. Recurrence of the frog model on the 3,2-alternating tree. https://arxiv.org/abs/1701.02813

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