Related papers: Correlation of sequences and of measures, generic …
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…
The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This…
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as an infinite sum of geometric terms. We present necessary conditions for the invariant measure…
We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_\infty$-invariant and concentrated on a single…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
Identifying the number of lags to include in an autoregressive model remains an open research problem due to the computational burden of treating it as a hyperparameter, especially in complex models. This study explores model-agnostic…
An investigation is presented of how a comprehensive choice of five most important measures of concordance (namely Spearman's rho, Kendall's tau, Gini's gamma, Blomqvist's beta, and their weaker counterpart Spearman's footrule) relate to…
In this paper we deal with an invariant ergodic hyperbolic measure $\mu$ for a diffeomorphism $f,$ assuming that $f$ it is either $C^{1+\alpha}$ or $f$ is $C^1$ and the Oseledec splitting of $\mu$ is dominated. We show that this system…
We consider ergodic $\mathrm{Sym}(\mathbb{N})$-invariant probability measures on the space of $L$-structures with domain $\mathbb{N}$ (for $L$ a countable relational language), and call such a measure a properly ergodic structure when no…
In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic sigma-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a…
We study attracting graphs of step skew products from the topological and ergodic points of view where the usual contracting-like assumptions of the fiber dynamics are replaced by weaker merely topological conditions. In this context, we…
We study the invariant measures and fluctuation limits of discrete-time harness processes in one spatial dimension. We construct one essential ergodic (under spatial shifts) invariant measure of the increment process derived from harness…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
After relating the notion of $\omega$-recurrence in skew products to the range of values taken by partial ergodic sums and Lyapunov exponents, ergodic $\mathbb{Z}$-valued cocycles over an irrational rotation are presented in detail. First,…
We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…
We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…
We investigate multiscale Gibbs measures from a variational and probabilistic viewpoint, focusing on the structural asymmetry among conditional entropies that characterizes their construction. We show how this asymmetry emerges both from…
We develop a robust structure theory for multiple ergodic averages of commuting transformations along Hardy sequences of polynomial growth. We then apply it to derive a number of novel results on joint ergodicity, recurrence and…