Terry Soo

Independent, but not identically distributed coin-flips

In joint work with Zemer Kosloff, we will discuss the dynamical properties of a seemingly innocuous perturbation of a sequence of independent and identically distributed (iid) coin-flips to one that is no longer stationary. In the stationary case, Ornstein proved that iid systems are completely classified up to isomorphism by their Shannon entropy. We will find that in the nonstationary case, the usual entropy theory no longer applies, but we will recover an explicit version of the Sinai factor theorem that allows us to generate iid randomness from a nonstationary source.