Abstract
Starting from the root, extend k branches and append k children with probability p, or terminate with probability q=1–p. Then, we have a finite k-ary tree with probability one if 0 ≤p ≤1/k. Moreover, we give the expectation and variance of the length of ideal codewords for representing the finite trees. Furthermore, we establish the probability of obtaining infinite tree, that is, of penetrating to infinity without termination for case 1/k ≤p ≤1.
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Kobayashi, K., Morita, H., Hoshi, M. (2006). Percolation on a k-Ary Tree. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_39
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DOI: https://doi.org/10.1007/11889342_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46244-6
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