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pro vyhledávání: '"Austin, Tim"'
Autor:
Austin, Tim
Let $S$ and $T$ be measure-preserving transformations of a probability space $(X,{\mathcal B},\mu)$. Let $f$ be a bounded measurable functions, and consider the integrals of the corresponding `double' ergodic averages: \[\frac{1}{n}\sum_{i=0}^{n-1} \
Externí odkaz:
http://arxiv.org/abs/2407.08630
We construct an explicit algebraic example of a subshift of finite type over a group $\Gamma$ with an invariant Markov measure which has completely positive sofic entropy (with respect to `most' sofic approximations) and yet does not have a direct Be
Externí odkaz:
http://arxiv.org/abs/2312.17387
An ergodic dynamical system $\mathbf{X}$ is called dominant if it is isomorphic to a generic extension of itself. It was shown in an earlier paper by Glasner, Thouvenot and Weiss that Bernoulli systems with finite entropy are dominant. In this work w
Externí odkaz:
http://arxiv.org/abs/2112.03800
Publikováno v:
In Journal of Safety Research June 2024 89:83-90
Autor:
Austin, Tim
Let $a < b$ be multiplicatively independent integers, both at least $2$. Let $A,B$ be closed subsets of $[0,1]$ that are forward invariant under multiplication by $a$, $b$ respectively, and let $C := A\times B$. An old conjecture of Furstenberg asser
Externí odkaz:
http://arxiv.org/abs/2009.01292
Autor:
Austin, Tim
Let $K_1$, $\dots$, $K_n$ be bounded, complete, separable metric spaces. Let $\lambda_i$ be a Borel probability measure on $K_i$ for each $i$. Let $f:\prod_i K_i \to \mathbb{R}$ be a bounded and continuous potential function, and let $$\mu(d \mathbf{
Externí odkaz:
http://arxiv.org/abs/1810.07278
Autor:
Austin, Tim
Publikováno v:
Kybernetika 56 (2020), no. 3, 459--499
Total correlation (`TC') and dual total correlation (`DTC') are two classical ways to quantify the correlation among an $n$-tuple of random variables. They both reduce to mutual information when $n=2$. The first part of this paper sets up the theory
Externí odkaz:
http://arxiv.org/abs/1809.10272
Autor:
Austin, Tim, Podder, Moumanti
Consider a statistical physical model on the $d$-regular infinite tree $T_{d}$ described by a set of interactions $\Phi$. Let $\{G_{n}\}$ be a sequence of finite graphs with vertex sets $V_n$ that locally converge to $T_{d}$. From $\Phi$ one can cons
Externí odkaz:
http://arxiv.org/abs/1705.03589
Autor:
Austin, Tim
Publikováno v:
This is a pre-print of an article published in Publ.math.IHES (2018). The final authenticated version is available online at: https://doi.org/10.1007/s10240-018-0098-3
Let $(X,\mu)$ be a standard probability space. An automorphism $T$ of $(X,\mu)$ has the weak Pinsker property if for every $\varepsilon > 0$ it has a splitting into a direct product of a Bernoulli shift and an automorphism of entropy less than $\vare
Externí odkaz:
http://arxiv.org/abs/1705.00302