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An extension of the cogrowth formula to arbitrary subsets of the tree
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What is the probability that a random walk in the free group ends in a proper power? Or in a primitive element? We present a formula that computes the exponential decay rate of the probability that a random walk on a regular tree ends in a given subset, in terms of the exponential decay rate of the analogous probability of the non-backtracking random walk. This generalizes the well-known cogrowth formula of Grigorchuk, Cohen and Northshield. We also extend the formula to arbitrary subsets of the biregular tree.
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Cited by 2 Pith papers
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Critical-exponent stratification and inverse realization on biregular trees
Free type-preserving actions on biregular trees realize every critical exponent up to (1/2)log(rs); finitely generated actions have a countable dense spectrum, and rank-two values equal roots of three explicit polynom...
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A note on Puder's generalised co-growth formula for trees
For any non-negative weighting on a (k,l)-bi-regular tree, the growth rate of all walks is determined by the growth rate of non-backtracking walks through Puder's conjectured formula.
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