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Displaying similar documents to “Infinite invariant measures for non-uniformely expanding transformations of [0, 1]: weak law of large numbers with anamalous scaling.”

Finiteness of Ergodic Unitarily Invariant Measures on Spaces of Infinite Matrices

Alexander I. Bufetov (2014)

Annales de l’institut Fourier

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The main result of this note, Theorem 1.3, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant and ergodic under the action of the infinite unitary group and that admits well-defined projections onto the quotient space of “corners" of finite size, must be finite. A similar result, Theorem 1.1, is also established for unitarily invariant measures on the space of all infinite complex matrices. These results imply that the infinite Hua-Pickrell...

On invariant measures for the tend map.

Francesc Bofill (1988)

Stochastica

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The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mu for each parameter value b. The continuity of the map b --> mu is established.

Invariant measures for piecewise convex transformations of an interval

Christopher Bose, Véronique Maume-Deschamps, Bernard Schmitt, S. Sujin Shin (2002)

Studia Mathematica

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We investigate the existence and ergodic properties of absolutely continuous invariant measures for a class of piecewise monotone and convex self-maps of the unit interval. Our assumption entails a type of average convexity which strictly generalizes the case of individual branches being convex, as investigated by Lasota and Yorke (1982). Along with existence, we identify tractable conditions for the invariant measure to be unique and such that the system has exponential decay of correlations...

Two Kinds of Invariance of Full Conditional Probabilities

Alexander R. Pruss (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let G be a group acting on Ω and ℱ a G-invariant algebra of subsets of Ω. A full conditional probability on ℱ is a function P: ℱ × (ℱ∖{∅}) → [0,1] satisfying the obvious axioms (with only finite additivity). It is weakly G-invariant provided that P(gA|gB) = P(A|B) for all g ∈ G and A,B ∈ ℱ, and strongly G-invariant provided that P(gA|B) = P(A|B) whenever g ∈ G and A ∪ gA ⊆ B. Armstrong (1989) claimed that weak and strong invariance are equivalent, but we shall show that this is false...

Tower multiplexing and slow weak mixing

Terrence Adams (2015)

Colloquium Mathematicae

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A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity sequences of weak mixing transformations. Namely, given any rigidity sequence for an ergodic measure preserving transformation, there exists a weak mixing transformation which is rigid along the same sequence. This establishes a wide range of rigidity sequences for weakly mixing dynamical...