A phase transition in random coin tossing

David A. Levin; Robin Pemantle; Yuval Peres

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A phase transition in random coin tossing

David A. Levin·Robin Pemantle·Yuval Peres

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Abstract

Suppose that a coin with bias theta is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let mu_θbe the distribution of the observed sequence of coin tosses, and let u_n denote the chance of a renewal at time n. Harris and Keane showed that if sum_{n=1}^infty u_n^2=\infty, then mu_theta and μ_0 are singular, while if sum_{n=1}^{infty} u_n^2 theta_c, they are singular. We also prove that when u_n=O(n^{-1}), the measures mu_theta for theta in [-1,1] are all mutually absolutely continuous.

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BibTeX RIS

David A. Levin, Robin Pemantle, Yuval Peres. 2004-04-05. A phase transition in random coin tossing. https://arxiv.org/abs/math/0404098

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