منابع مشابه
Reversible Markov structures on divisible set partitions
We study k-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integer k = 1, 2, . . .. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, for k > 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is ne...
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We prove that a general class of expansive Z d-actions by automorphisms of compact, abelian groups with completely positive en-tropy has`symbolic covers' of equal topological entropy. These symbolic covers are constructed by using homoclinic points of these actions. For d = 1 we adapt a result of Kenyon and Vershik in 7] to prove that these symbolic covers are, in fact, sooc shifts. For d 2 we ...
متن کاملSymbolic Dynamics and Markov Partitions
The decimal expansion of real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a genera...
متن کاملConvergence rates of Markov chains on spaces of partitions ∗
We study the convergence rate to stationarity for a class of exchangeable partitionvalued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain is determined by products of i.i.d. stochastic matrices, which describe the chain induced on the simplex by taking asymptotic frequencies. Using this representation, we establish upper bounds for the mixin...
متن کاملNon-normal numbers with respect to Markov partitions
We call a real number normal if for any block of digits the asymptotic frequency of this block in the N -adic expansion equals the expected one. In the present paper we consider non-normal numbers and, in particular, essentially and extremely non-normal numbers. We call a real number essentially non-normal if for each single digit there exists no asymptotic frequency of its occurrence. Furtherm...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1985
ISSN: 0387-3870
DOI: 10.3836/tjm/1270151581