Monotone factors of I.I.D. processes

摘要

LetB(p) andB(q) be Bernoulli shifts on {0, 1,...,d - 1}ℤ. Ifh(p)>h(q), it is a classical theorem of Sinai that there is a factor map takingB(p) toB(q). If, in addition,p stochastically dominatesq, we can ask whether there is such a factor map ϕ which is monotone: ϕ(x) i≤xi for each coordinatei of almost every pointx. Here we show that there is a monotone finitary code fromB(p) toB(q) in the case whereB(q) is a shift on two symbols.