Exploiting approximate transitivity of trust

2007 ◽  
Author(s):  
Ruggero Morselli ◽  
Bobby Bhattacharjee ◽  
Jonathan Katz ◽  
Michael Marsh
Keyword(s):  
Approximate Transitivity

scholarly journals Approximate transitivity property and Lebesgue spectrum

2010 ◽  
Vol 161 (2) ◽  
pp. 121-144 ◽  
Author(s):  
E. H. El Abdalaoui ◽  
M. Lemańczyk
Keyword(s):  
Lebesgue Spectrum ◽  
Transitivity Property ◽  
Approximate Transitivity

scholarly journals Nearly Approximate Transitivity (AT) for Circulant Matrices

2019 ◽  
Vol 71 (2) ◽  
pp. 381-415
Author(s):  
David Handelman
Keyword(s):  
Topological Dynamics ◽  
Circulant Matrices ◽  
Discrete Groups ◽  
Dimension Group ◽  
Dimension Space ◽  
Approximate Transitivity

AbstractBy previous work of Giordano and the author, ergodic actions of $\mathbf{Z}$ (and other discrete groups) are completely classified measure-theoretically by their dimension space, a construction analogous to the dimension group used in $\text{C}^{\ast }$-algebras and topological dynamics. Here we investigate how far from approximately transitive (AT) actions can be that derive from circulant (and related) matrices. It turns out not very: although non-AT actions can arise from this method of construction, under very modest additional conditions, approximate transitivity arises. KIn addition, if we drop the positivity requirement in the isomorphism of dimension spaces, then all these ergodic actions satisfy an analogue of AT. Many examples are provided.

Approximate transitivity of the ergodic action of the group of finite permutations of on

2018 ◽  
Vol 39 (11) ◽  
pp. 2881-2895
Author(s):  
B. MITCHELL BAKER ◽  
THIERRY GIORDANO ◽  
RADU B. MUNTEANU
Keyword(s):  
Symmetric Group ◽  
Product Space ◽  
Ergodic Action ◽  
Probability Measures ◽  
Natural Action ◽  
Bernoulli Measure ◽  
Approximate Transitivity

In this paper we show that the natural action of the symmetric group acting on the product space $\{0,1\}^{\mathbb{N}}$ endowed with a Bernoulli measure is approximately transitive. We also extend the result to a larger class of probability measures.

scholarly journals Approximately transitive flows and ITPFI factors

1985 ◽  
Vol 5 (2) ◽  
pp. 203-236 ◽  
Author(s):  
A. Connes ◽  
E. J. Woods
Keyword(s):  
Lebesgue Measure ◽  
Group Action ◽  
Measure Space ◽  
Finite Measure ◽  
Type Iii ◽  
Ergodic Transformations ◽  
Zero Entropy ◽  
Approximate Transitivity

AbstractWe define a new property of a Borel group action on a Lebesgue measure space, which we call approximate transitivity. Our main results are (i) a type III0 hyperfinite factor is ITPFI if and only if its flow of weights is approximately transitive, and (ii) for ergodic transformations preserving a finite measure, approximate transitivity implies zero entropy.

Approximate transitivity for zero-entropy systems

2005 ◽  
Vol 25 (2) ◽  
pp. 443-453 ◽  
Author(s):  
ANTHONY DOOLEY ◽  
ANTHONY QUAS
Keyword(s):  
Zero Entropy ◽  
Approximate Transitivity
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