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pro vyhledávání: '"CREUTZ, DARREN"'
Autor:
Creutz, Darren, Pavlov, Ronnie
We prove that every infinite minimal subshift with word complexity $p(q)$ satisfying $\limsup p(q)/q < 3/2$ is measure-theoretically isomorphic to its maximal equicontinuous factor; in particular, it has measurably discrete spectrum. Among other appl
Externí odkaz:
http://arxiv.org/abs/2308.14901
Autor:
Creutz, Darren, Pavlov, Ronnie
We prove results about subshifts with linear (word) complexity, meaning that $\limsup \frac{p(n)}{n} < \infty$, where for every $n$, $p(n)$ is the number of $n$-letter words appearing in sequences in the subshift. Denoting this limsup by $C$, we show
Externí odkaz:
http://arxiv.org/abs/2302.10336
Autor:
Creutz, Darren
We resolve a long-standing open question on the relationship between measure-theoretic dynamical complexity and symbolic complexity by establishing the exact word complexity at which measure-theoretic strong mixing manifests: For every superlinear $f
Externí odkaz:
http://arxiv.org/abs/2206.10047
Autor:
Creutz, Darren
Publikováno v:
Ergod. Th. Dynam. Sys. 44 (2024) 1330-1366
We exhibit subshifts admitting weakly mixing (probability) measures, for arbitrary $\epsilon > 0$, with word complexity $p$ satisfying $\limsup \frac{p(q)}{q} < 1.5 + \epsilon$. For arbitrary $f(q) \to \infty$, said subshifts can be made to satisfy $
Externí odkaz:
http://arxiv.org/abs/2205.08691
We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any $f : \mathbb{N} \to \mathbb{N}$ with $f(n)/n$ increasing and $\sum 1/f(n) <
Externí odkaz:
http://arxiv.org/abs/2201.00489
Autor:
Creutz, Darren
A compactly generated group is noncompact if and only if it admits a nonconstant harmonic function (for some, equivalently for every, reasonable measure). This generalizes the known fact that a finitely generated group is infinite if and only if it a
Externí odkaz:
http://arxiv.org/abs/2012.07948
Autor:
Creutz, Darren
Every stationary action of a strongly irreducible lattice or commensurator of such a latiice in a general semisimple group, with at least one higher-rank connected factor, either has finite stabilizers almost surely or finite index stabilizers almost
Externí odkaz:
http://arxiv.org/abs/2010.13987
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Autor:
Creutz, Darren
We present an exposition of contractive spaces and of relatively contractive maps. Contractive spaces are the natural opposite of measure-preserving actions and relatively contractive maps the natural opposite of relatively measure-preserving maps. T
Externí odkaz:
http://arxiv.org/abs/1508.01561
Akademický článek
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