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Some Properties of Markov chains on the Free Group F2.
- Source :
- Journal of Theoretical Probability; Sep2024, Vol. 37 Issue 3, p2330-2351, 22p
- Publication Year :
- 2024
-
Abstract
- Random walks cannot, in general, be pushed forward by quasi-isometries. Tame Markov chains were introduced as a 'quasi-isometry invariant' generalization of random walks. In this paper, we construct several examples of tame Markov chains on the free group exhibiting 'exotic' behavior; one, where the drift is not well defined and one where the drift is well defined but the Central Limit Theorem does not hold. We show that this is not a failure of the notion of tame Markov chain, but rather that any quasi-isometry invariant theory that generalizes random walks will include examples without well-defined drift. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08949840
- Volume :
- 37
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Journal of Theoretical Probability
- Publication Type :
- Academic Journal
- Accession number :
- 179042039
- Full Text :
- https://doi.org/10.1007/s10959-023-01294-1