scholarly journals Topological Entropy for Arbitrary Subsets of Infinite Product Spaces

2022 ◽  
Author(s):  
Maysam Maysami Sadr ◽  
Mina Shahrestani
Keyword(s):  
Topological Entropy ◽  
Infinite Product ◽  
Product Spaces

A Comparison of Methods for Constructing Probability Measures on Infinite Product Spaces

1987 ◽  
Vol 30 (3) ◽  
pp. 282-285 ◽  
Author(s):  
Charles W. Lamb
Keyword(s):  
Probability Measure ◽  
Conditional Probability ◽  
Product Space ◽  
Infinite Product ◽  
Probability Measures ◽  
Classical Theorem ◽  
Comparison Of Methods ◽  
Product Spaces ◽  
Probability Functions ◽  
Finite Dimensional

AbstractThe construction, from a consistent family of finite dimensional probability measures, of a probability measure on a product space when the marginal measures are perfect is shown to follow from a classical theorem due to Ionescu Tulcea and known results on the existence of regular conditional probability functions.

scholarly journals Odometer action on Riesz product

1996 ◽  
Vol 61 (2) ◽  
pp. 143-149
Author(s):  
Masamichi Yoshida
Keyword(s):  
Dynamical Systems ◽  
Constant Coefficient ◽  
Infinite Product ◽  
Product Spaces ◽  
Riesz Product ◽  
Ratio Set

AbstractWe consider the Riesz product with a constant coefficient and odometer action over infinite product spaces. By studying the ratio set we can conclude the type of the above dynamical systems is III1.

scholarly journals Asymptotics of locally-interacting Markov chains with global signals

2002 ◽  
Vol 34 (2) ◽  
pp. 416-440
Author(s):  
Ulrich Horst
Keyword(s):  
Markov Chains ◽  
Random Systems ◽  
Infinite Product ◽  
Sufficient Conditions ◽  
Convergence Result ◽  
Microscopic Level ◽  
Product Spaces ◽  
Macroscopic Level ◽  
Long Run ◽  
Sufficient Conditions For Convergence

We study the long-run behaviour of interactive Markov chains on infinite product spaces. The behaviour at a single site is influenced by the local situation in some neighbourhood and by a random signal about the average situation throughout the whole system. The asymptotic behaviour of such Markov chains is analyzed on the microscopic level and on the macroscopic level of empirical fields. We give sufficient conditions for convergence on the macroscopic level. Combining a convergence result from the theory of random systems with complete connections with a perturbation of the Dobrushin-Vasserstein contraction technique, we show that macroscopic convergence implies that the underlying microscopic process has local asymptotic loss of memory.

scholarly journals Asymptotics of locally-interacting Markov chains with global signals

2002 ◽  
Vol 34 (02) ◽  
pp. 416-440 ◽  
Author(s):  
Ulrich Horst
Keyword(s):  
Markov Chains ◽  
Random Systems ◽  
Infinite Product ◽  
Sufficient Conditions ◽  
Convergence Result ◽  
Microscopic Level ◽  
Product Spaces ◽  
Macroscopic Level ◽  
Long Run ◽  
Sufficient Conditions For Convergence

We study the long-run behaviour of interactive Markov chains on infinite product spaces. The behaviour at a single site is influenced by the local situation in some neighbourhood and by a random signal about the average situation throughout the whole system. The asymptotic behaviour of such Markov chains is analyzed on the microscopic level and on the macroscopic level of empirical fields. We give sufficient conditions for convergence on the macroscopic level. Combining a convergence result from the theory of random systems with complete connections with a perturbation of the Dobrushin-Vasserstein contraction technique, we show that macroscopic convergence implies that the underlying microscopic process has local asymptotic loss of memory.

Computing the critical dimensions of Bratteli–Vershik systems with multiple edges

2011 ◽  
Vol 32 (1) ◽  
pp. 103-117 ◽  
Author(s):  
ANTHONY H. DOOLEY ◽  
RIKA HAGIHARA
Keyword(s):  
Growth Rate ◽  
Dynamical Systems ◽  
Infinite Product ◽  
Critical Dimension ◽  
Product Spaces ◽  
Critical Dimensions ◽  
Multiple Edges

AbstractThe critical dimension is an invariant that measures the growth rate of the sums of Radon–Nikodym derivatives for non-singular dynamical systems. We show that for Bratteli–Vershik systems with multiple edges, the critical dimension can be computed by a formula analogous to the Shannon–McMillan–Breiman theorem. This extends earlier results of Dooley and Mortiss on computing the critical dimensions for product and Markov odometers on infinite product spaces.

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