Tim Austin
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View article: Implementing an integrated psychological and physical intervention in routine physiotherapy practice for patients with musculoskeletal road traffic injury: protocol for a hybrid implementation-effectiveness type III cluster randomised controlled trial
Implementing an integrated psychological and physical intervention in routine physiotherapy practice for patients with musculoskeletal road traffic injury: protocol for a hybrid implementation-effectiveness type III cluster randomised controlled trial Open
ACTRN12624001268538. Registered on 18 October 2024. https://www.anzctr.org.au/Trial/Registration/TrialReview.aspxid=388006&showOriginal=true&isReview=true.
View article: Annealed almost periodic entropy
Annealed almost periodic entropy Open
This work studies certain notions of entropy that can be associated to (i) a representation of a separable, unital C*-algebra $\mathfrak{A}$ and (ii) an auxiliary random sequence $(π_n)_{n\ge 1}$ of finite-dimensional representations of $\…
View article: ALGEBRAIC DYNAMICAL SYSTEMS FROM LDPC CODES SATISFY A STRONG NEGATION OF THE WEAK PINSKER PROPERTY
ALGEBRAIC DYNAMICAL SYSTEMS FROM LDPC CODES SATISFY A STRONG NEGATION OF THE WEAK PINSKER PROPERTY Open
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…
View article: Entropy and determinants for unitary representations
Entropy and determinants for unitary representations Open
Several notions of entropy have been studied widely in the ergodic theory of probability-preserving actions of countable groups. These include the generalization of Kolmogorov--Sinai entropy to amenable groups based on Følner sequences, pe…
View article: Non-convergence of some non-commuting double ergodic averages
Non-convergence of some non-commuting double ergodic averages Open
Let $S$ and $T$ be measure-preserving transformations of a probability space $(X,{\mathcal B},μ)$. Let $f$ be a bounded measurable functions, and consider the integrals of the corresponding `double' ergodic averages: \[\frac{1}{n}\sum_{i=0…
View article: Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property
Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property Open
We construct an explicit algebraic example of a subshift of finite type over a group $Γ$ with an invariant Markov measure which has completely positive sofic entropy (with respect to `most' sofic approximations) and yet does not have a dir…
View article: An ergodic system is dominant exactly when it has positive entropy
An ergodic system is dominant exactly when it has positive entropy Open
An ergodic dynamical system $\mathbf {X}$ is called dominant if it is isomorphic to a generic extension of itself. It was shown by Glasner et al [On some generic classes of ergodic measure preserving transformations. Trans. Moscow Math. So…
View article: A new dynamical proof of the Shmerkin–Wu theorem
A new dynamical proof of the Shmerkin–Wu theorem Open
Let be multiplicatively independent integers, both at least . Let be closed subsets of that are forward invariant under multiplication by , respectively, and let . An old conjecture of Furstenberg asserted that any planar line not par…
View article: An ergodic system is dominant exactly when it has positive entropy
An ergodic system is dominant exactly when it has positive entropy Open
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 …
View article: INCEFA-PLUS Findings on Environmental Fatigue
INCEFA-PLUS Findings on Environmental Fatigue Open
INCEFA-PLUS is a five year project supported by the European Commission HORIZON2020 programme. The project concluded in October 2020. 16 organisations from across Europe have combined forces to deliver new experimental data which is being …
View article: The structure of low-complexity Gibbs measures on product spaces
The structure of low-complexity Gibbs measures on product spaces Open
Let $K_1$, $\dots$, $K_n$ be bounded, complete, separable metric spaces. Let $λ_i$ 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 $$μ(d \math…
View article: Measures of correlation and mixtures of product measures.
Measures of correlation and mixtures of product measures. Open
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 …
View article: The Geometry of Model Spaces forProbability-Preserving Actions of SoficGroups
The Geometry of Model Spaces forProbability-Preserving Actions of SoficGroups Open
Bowen’s notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the ‘model sp…
View article: The Geometry of Model Spaces forProbability-Preserving Actions of SoficGroups
The Geometry of Model Spaces forProbability-Preserving Actions of SoficGroups Open
Bowen’s notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the ‘model sp…
View article: Integrable measure equivalence for groups of polynomial growth
Integrable measure equivalence for groups of polynomial growth Open
Bader, Furman and Sauer have recently introduced the notion of integrable measure equivalence for nitely-generated groups. is is the sub-equivalence relation of measure equivalence obtained by insisting that the relevant cocycles satisfy a…
View article: ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES
ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES Open
Sofic entropy is an invariant for probability-preserving actions of sofic groups. It was introduced a few years ago by Lewis Bowen, and shown to extend the classical Kolmogorov–Sinai entropy from the setting of amenable groups. Some parts …
View article: Quantitative Equidistribution for Certain Quadruples in Quasi-Random Groups: Erratum
Quantitative Equidistribution for Certain Quadruples in Quasi-Random Groups: Erratum Open
In my recent paper [1] there is a mistake in the proof of Corollary 3. The first line of the displayed equation in that proof asserts that \[\int_G|\langle u,\pi^g v\rangle_V|^2\,\rm{d} g = \int_G\langle u\otimes u,(\pi^g\otimes \pi^g)(v\o…
View article: Ajtai-Szemerédi Theorems over quasirandom groups
Ajtai-Szemerédi Theorems over quasirandom groups Open
Two versions of the Ajtai-Szemerédi Theorem are considered in the Cartesian square of a finite non-Abelian group $G$. In case $G$ is sufficiently quasirandom, we obtain strong forms of both versions: if $E \subseteq G\times G$ is fairly de…