Tail fields generated by symbol counts in measure-preserving systems

Karl Petersen ¹   ; Jean-Paul Thouvenot ²

¹ Department of Mathematics University of North Carolina CB 3250, Phillips Hall Chapel Hill, NC 27599 U.S.A.
² Laboratoire de Probabilités Université Pierre et Marie Curie 4 place Jussieu, 75252 Paris, France

Colloquium Mathematicum, Tome 101 (2004) no. 1, pp. 9-23

Résumé

A finite-state stationary process is called (one- or two-sided) super-$K$ if its (one- or two-sided) super-tail field—generated by keeping track of (initial or central) symbol counts as well as of arbitrarily remote names—is trivial. We prove that for every process $(\alpha,T)$ which has a direct Bernoulli factor there is a generating partition $\beta$ whose one-sided super-tail equals the usual one-sided tail of $\beta$. Consequently, every $K$-process with a direct Bernoulli factor has a one-sided super-$K$ generator. (This partially answers a question of Petersen and Schmidt.)

Détail

DOI : 10.4064/cm101-1-2

Keywords: finite state stationary process called one two sided super k its one two sided super tail field generated keeping track initial central symbol counts arbitrarily remote names trivial prove every process alpha which has direct bernoulli factor there generating partition beta whose one sided super tail equals usual one sided tail nbsp beta consequently every k process direct bernoulli factor has one sided super k generator partially answers question petersen schmidt