Entropy-efficient finitary codings by IID processes

A process Y is a factor of a process X if it can be written as Y=F(X) for some function F which commutes with translations. The factor is finitary if Y_0 is almost surely determined by some finite portion of the input X. Given a process Y, the question of whether Y is a (finitary) factor of an IID process is fundamental in ergodic theory and has received much attention in probability as well. As it turns out, contrary to the prevailing belief, some classical results about factors do not have finitary counterparts, as was recently shown by Gabor. We will present a complementary result that any process Y which is a finitary factor of an IID process furthermore admits an entropy-efficient finitary coding by an IID process. Here entropy-efficient means that the IID process has entropy arbitrarily close to that of Y. As an application we give an affirmative answer to an old question of van den Berg and Steif about the critical Ising model.

Joint work with Tom Meyerovitch.

October 13, 3PM, ESB 4133 (PIMS library) hybrid (if in person, please wear a mask)

https://ubc.zoom.us/j/65209400719?pwd=OFF1K2h5VGtFZFhyRFFWNm1vTW5RUT09

Meeting ID: 652 0940 0719
Passcode: 858749