Fast simulation of new coins from old

Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the problem of using independent tosses of a coin with probability of heads p (where p\in S is unknown) to simulate a coin with probability of heads f(p). We prove that if S is a closed interval and f is real analytic on S, then f...

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Veröffentlicht in:arXiv.org 2005-03
Hauptverfasser: Nacu, Serban, Peres, Yuval
Format: Artikel
Sprache:eng
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Zusammenfassung:Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the problem of using independent tosses of a coin with probability of heads p (where p\in S is unknown) to simulate a coin with probability of heads f(p). We prove that if S is a closed interval and f is real analytic on S, then f has a fast simulation on S (the number of p-coin tosses needed has exponential tails). Conversely, if a function f has a fast simulation on an open set, then it is real analytic on that set.
ISSN:2331-8422
DOI:10.48550/arxiv.0309222