Results 1  10
of
48
ON THE SUBADDITIVE ERGODIC THEOREM
"... Abstract. We present a simple proof of Kingman’s Subadditive Ergodic Theorem that does not rely on Birkhoff’s (Additive) Ergodic Theorem and therefore yields it as a corollary. 1. Statements Throughout this note, let (X,A, µ) be a fixed probability space and T: X → X be a fixed measurable map that ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We present a simple proof of Kingman’s Subadditive Ergodic Theorem that does not rely on Birkhoff’s (Additive) Ergodic Theorem and therefore yields it as a corollary. 1. Statements Throughout this note, let (X,A, µ) be a fixed probability space and T: X → X be a fixed measurable map
SUBADDITIVE ERGODIC THEOREMS FOR RANDOM SETS IN INFINITE DIMENSIONS
, 1998
"... We prove pointwise and mean versions of the subadditive ergodic theorem for superstationary families of compact, convex random subsets of a real Banach space, extending previously known results that were obtained in nite dimensions or with additional hypotheses on the random sets. We also show how ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We prove pointwise and mean versions of the subadditive ergodic theorem for superstationary families of compact, convex random subsets of a real Banach space, extending previously known results that were obtained in nite dimensions or with additional hypotheses on the random sets. We also show
Rate of convergence of the mean for subadditive ergodic sequences
, 2014
"... For subadditive ergodic processes {Xm,n} with weak dependence, we analyze the rate of convergence of EX0,n/n to its limit g. We define an exponent γ given roughly by EX0,n ∼ ng + nγ, and, assuming existence of a fluctuation exponent χ that gives VarX0,n ∼ n2χ, we provide a lower bound for γ of the ..."
Abstract
 Add to MetaCart
For subadditive ergodic processes {Xm,n} with weak dependence, we analyze the rate of convergence of EX0,n/n to its limit g. We define an exponent γ given roughly by EX0,n ∼ ng + nγ, and, assuming existence of a fluctuation exponent χ that gives VarX0,n ∼ n2χ, we provide a lower bound for γ
The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms
, 2005
"... Given a free group Fk of rank k ≥ 2 with a fixed set of free generators we associate to any homomorphism φ from Fk to a group G with a leftinvariant seminorm a generic stretching factor, λ(φ), which is a noncommutative generalization of the translation number. We concentrate on the situation when ..."
Abstract

Cited by 26 (11 self)
 Add to MetaCart
Given a free group Fk of rank k ≥ 2 with a fixed set of free generators we associate to any homomorphism φ from Fk to a group G with a leftinvariant seminorm a generic stretching factor, λ(φ), which is a noncommutative generalization of the translation number. We concentrate on the situation when φ: Fk → Aut(X) corresponds to a free action of Fk on a simplicial tree X, in particular, when φ corresponds to the action of Fk on its Cayley graph via an automorphism of Fk. In this case we are able to obtain some detailed “arithmetic ” information about the possible values of λ = λ(φ).
Linear repetitivity, I. Uniform subadditive ergodic theorems and applications, Discrete Comput
 Geom
"... Abstract. This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive ergodic theorems on tilings. The results of this pa ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive ergodic theorems on tilings. The results
Ergodic Theorems for Subadditive Superstationary Families of Random Sets with Values in Banach Spaces
, 1996
"... Pointwise and mean ergodic theorems under different assumptions for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize the results of [14], where random sets in R d are c ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Pointwise and mean ergodic theorems under different assumptions for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize the results of [14], where random sets in R d
UNIFORM SUBADDITIVE ERGODIC THEOREM ON APERIODIC LINEARLY REPETITVE TILINGS AND APPLICATIONS
, 2007
"... Abstract: The paper is concerned with aperiodic linearly repetitive tilings. For such tilings we establish a weak form of selfsimilarity that allows us to prove general (sub)additive ergodic theorems. Finally, we provide applications to the study of lattice gas models. 1 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract: The paper is concerned with aperiodic linearly repetitive tilings. For such tilings we establish a weak form of selfsimilarity that allows us to prove general (sub)additive ergodic theorems. Finally, we provide applications to the study of lattice gas models. 1
SEMIUNIFORM SUBADDITIVE ERGODIC THEOREMS FOR DISCONTINUOUS SKEWPRODUCT TRANSFORMATIONS
"... Abstract. In this paper we will establish some semiuniform ergodic theorems for skewproduct transformations with discontinuity from the point of view of topology. The main assumptions are that the discontinuity sets of transformations are neglected in some measuretheoretical sense. The theorems ..."
Abstract
 Add to MetaCart
Abstract. In this paper we will establish some semiuniform ergodic theorems for skewproduct transformations with discontinuity from the point of view of topology. The main assumptions are that the discontinuity sets of transformations are neglected in some measuretheoretical sense. The theorems
Observable Optimal State Points of Subadditive Potentials
"... For a sequence of subadditive potentials, a method of choosing state points with negative growth rates for an ergodic dynamical system was given in [5]. This paper first generalizes this result to the nonergodic dynamics, and then proves that under some mild additional hypothesis, one can choose po ..."
Abstract
 Add to MetaCart
For a sequence of subadditive potentials, a method of choosing state points with negative growth rates for an ergodic dynamical system was given in [5]. This paper first generalizes this result to the nonergodic dynamics, and then proves that under some mild additional hypothesis, one can choose
Results 1  10
of
48