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Norm convergence of nilpotent ergodic averages
(Annal Mathematics, 2012-05)
We show that multiple polynomial ergodic averages arising from nilpo-tent groups of measure preserving transformations of a probability space always converge in the L 2 norm.
Convergence in the Cesàro sense of ergodic operators associated with a flow
(Univ Illinois Urbana-champaign, 2000-09)
We study the a.e. convergence of the Cesàro-$(1+\alpha)$ ergodic averages and the a.e. existence in the Cesàro-$\alpha$ sense of the ergodic Hilbert transform associated with Cesàro bounded flow and $-1\lt \alpha \leq 0$.
Ergodic-nonergodic transition in tapped granular systems: The role of persistent contacts
(Instituto de Física de Líquidos y Sistemas Biológicos, 2016-01)
Static granular packs have been studied in the last three decades in the frame of a modified equilibrium statistical mechanics that assumes ergodicity as a basic postulate. The canonical example on which this framework is ...
About the concept of quantum chaos
(Molecular Diversity Preservation International, 2017-05)
The research on quantum chaos finds its roots in the study of the spectrum of complex nuclei in the 1950s and the pioneering experiments in microwave billiards in the 1970s. Since then, a large number of new results was ...
Detailed structure of configuration space and its importance on ergodic separation of ±J Ising lattices
(Elsevier Science, 2002-07-15)
A complete and exact characterization of the configuration space of 2-D ±J Ising lattices is performed. A new algorithm is introduced here representing advantages for reaching all states for small samples and doing a ...
The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
(Royal Society of Edinburgh, 2007-07)
Recently, Sarrión and the authors gave a sufficient condition on invertible Lamperti operators on Lp which guarantees the convergence in the Cesàro-α sense of the ergodic averages and the ergodic Hilbert transform for all ...
Sharp bound for the ergodic maximal operator associated to Cesàro bounded operators
(Academic Press Inc Elsevier Science, 2018-06)
We consider positive invertible Lamperti operators Tf(x)=h(x)Φf(x) such that Φ has no periodic part. Let An,T be the sequence of averages of T and MT the ergodic maximal operator. It is obvious that if MT is bounded on some Lp, 1
Ergodic nonergodic transition in tapped granular systems; The role of persistent contacts
(Papers in Physics, 2018)
Ergodic theorem in CAT(0) spaces in terms of inductive means
(Cambridge University Press, 2022-03)
Let (G, +) be a compact, abelian, and metrizable topological group. In this group we take g ∈ G such that the corresponding automorphism τg is ergodic. The main result of this paper is a new ergodic theorem for functions ...
Ergodic transforms associated to general averages
(Polish Academy of Sciences. Institute of Mathematics, 2010)