Related papers: Sofic Entropy of Gaussian Actions
This paper focuses on a stochastic formulation of Bayesian attitude estimation on the special orthogonal group. In particular, an exponential probability density model for random matrices, referred to as the matrix Fisher distribution is…
The notion of topological entropy is originally defined for a single action. Later it was extended by Kieffer for arbitrary discrete amenable groups. Recently Friedland defined topological entropy for any discrete group actions amenable or…
We say that a countable discrete group action $\alpha$ on a C$^*$-algebra $A$ is \textit{$\mathcal{W}$-absorbing} if there exist a C$^*$-algebra $B$ and an action $\beta$ on $B$ such that $\alpha$ is cocycle conjugate to $\beta\otimes…
It was proved by Brudno that entropy and Kolmogorov complexity for dynamical systems are tightly related. We generalize his results to the case of arbitrary computable amenable group actions. Namely, for an ergodic shift-action, the…
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on…
A recent result of Frantzikinakis establishes sufficient conditions for joint ergodicity in the setting of $\mathbb{Z}$-actions. We generalize this result for actions of second-countable locally compact abelian groups. We obtain two…
We consider a random walk $S_k$ with i.i.d. steps on a compact group equipped with a bi-invariant metric. We prove quantitative ergodic theorems for the sum $\sum_{k=1}^N f(S_k)$ with H\"older continuous test functions $f$, including the…
We look at group actions on metric spaces, particularly at group actions on geodesic hyperbolic spaces. We classify the types of automorphisms on these spaces and prove several results about the density of the hyperbolic limit set of the…
We develop in this paper some general techniques to analyze action sets of small doubling for probability measure-preserving actions of amenable groups. As an application of these techniques, we prove a dynamical generalization of Kneser's…
In this paper we show that the minimal value of Furstenberg entropy (along all measures, not restricting to stationary ones) for any amenable action is the same as for the action of the group on itself. Using the boundary amenability result…
By looking at the relationship between the recurrence properties of a countable group action with a quasi-invariant measure and the structure of its ergodic components we establish a simple general description of the Hopf decomposition of…
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…
Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional $S_{BG}[p(x)]…
The effective action formalism of quantum field theory is used to study the properties of the non-relativistic interacting Bose gas. The Gaussian approximation is formulated by calculating the effective action to the first order of the…
Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…
The entropies of molecules in solution are routinely calculated using gas phase formulae. It is assumed that, because implicit solvation models are fitted to reproduce free energies, this is sufficient for modeling reactions in solution.…
In this note we do the analysis of entanglement entropy more carefully when the non-conformal theory flows to a non-trivial IR fixed point. In particular we emphasize the role of the trace of the energy-momentum tensor in these…
It is well known that if $G$ is a countable amenable group and $G \curvearrowright (Y, \nu)$ factors onto $G \curvearrowright (X, \mu)$, then the entropy of the first action must be greater than or equal to the entropy of the second action.…