Sofic random processes
-
Wolfgang Krieger
and
Benjamin Weiss
Abstract
For a finite alphabet Σ, a subshift Y ⊂ Σℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y, ν) are the conditional measures of ν on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy.
©[2012] by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Conformal maps from a 2-torus to the 4-sphere
- Sofic random processes
- Overlap properties of geometric expanders
- Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8
- A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
- Spin representations of Weyl groups and the Springer correspondence
- Higgs bundles over the good reduction of a quaternionic Shimura curve
Articles in the same Issue
- Conformal maps from a 2-torus to the 4-sphere
- Sofic random processes
- Overlap properties of geometric expanders
- Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8
- A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
- Spin representations of Weyl groups and the Springer correspondence
- Higgs bundles over the good reduction of a quaternionic Shimura curve
