Iteration entropy
Number Theory
2017-12-20 v2
Abstract
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to \log_2(n) minus the entropy of the vector of its cycle lengths. For general functions, a similar approximation holds.
Keywords
Cite
@article{arxiv.1712.01407,
title = {Iteration entropy},
author = {Joachim von zur Gathen},
journal= {arXiv preprint arXiv:1712.01407},
year = {2017}
}
Comments
In Version 2, the definition of iteration entropy is modified by subtracting log_2(n) from it. This simplifies some expressions