| A Phase Transition in Random Coin Tossing (2007) | |||||||||||||||
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| this paper is organized as follows. In Section 2, we provide definitions and introduce notation. In Section 3, we prove a useful general zero-one law, to show that singularity and absolute continuity of the measures are the only possibilities. In Section 4, Theorem 1.1(i) is proved, while Theorem 1.1(ii) is established in Section 5. We prove a more general version of Theorem 1.2 in Section 6. In Section 7, we prove a criterion for absolute continuity, which is used to prove Theorem 1.4 in Section 8 and Theorem 1.3 in Section 9. A connection to long-range percolation and some unsolved problems are described in Section 10. Random Coin Tossing 7 2. Definitions. Let # = | |||||||||||||||
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