23 citations · 65 across the 22 of their papers we have counts for
11 papers · 1 filter
Mixing and equipartition for automorphism invariant processes on regular trees
Felix Pogorzelski, Elias Zimmermann
The paper is devoted to equipartition of measured information for finite state processes over regular trees whose laws are invariant under all parity preserving tree automorphisms.…
Shannon-McMillan-Breiman theorem along almost geodesics in negatively curved groups
Amos Nevo, Felix Pogorzelski
Consider a non-elementary Gromov-hyperbolic group with a suitable invariant hyperbolic metric, and an ergodic probability measure preserving (p.m.p.) action on . We cons…
Strict irreducibility of Markov chains and ergodicity of skew products
Pablo Lummerzheim, Felix Pogorzelski, Elias Zimmermann
We consider a family of measure preserving transformations, which act on a common probability space and are chosen at random by a stationary ergodic Markov chain. This setting defi…
Symbolic substitution systems beyond abelian groups
Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
In this article we construct the first examples of strongly aperiodic linearly repetitive Delone sets in non-abelian Lie groups by means of symbolic substitutions. In particular, w…
Aperiodic order and spherical diffraction, III: The shadow transform and the diffraction formula
Michael Björklund, Tobias Hartnick, Felix Pogorzelski
We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of…
Linear repetitivity beyond abelian groups
Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weig…
Delone dynamical systems and spectral convergence
Siegfried Beckus, Felix Pogorzelski
In the realm of Delone sets in locally compact, second countable, Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured qu…
Aperiodic order and spherical diffraction, II: Translation bounded measures on homogeneous spaces
Michael Björklund, Tobias Hartnick, Felix Pogorzelski
We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we stu…
The Shannon-McMillan-Breiman theorem beyond amenable groups
Amos Nevo, Felix Pogorzelski
We introduce a new isomorphism-invariant notion of entropy for measure preserving actions of arbitrary countable groups on probability spaces, which we call orbital Rokhlin entropy…
Aperiodic order and spherical diffraction, I: Auto-correlation of model sets
Michael Björklund, Tobias Hartnick, Felix Pogorzelski
We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally com…
Almost-additive ergodic theorems for amenable groups
Felix Pogorzelski
In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By ext…