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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 ..."
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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 ..."
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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
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 ..."
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Cited by 3 (2 self)
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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
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 ..."
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Cited by 26 (11 self)
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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).
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 ..."
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Cited by 1 (1 self)
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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
Cooperative strategies and capacity theorems for relay networks
 IEEE TRANS. INFORM. THEORY
, 2005
"... Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decodeandforward the source message to the destination, or they compressandforward their channel outputs to the destination. The decodeandforward scheme is a variant of ..."
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Cited by 739 (19 self)
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outputs and the destination’s channel output. The strategies are applied to wireless channels, and it is shown that decodeandforward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides
Uniform ergodic theorems on subshifts over a finite alphabet
 Ergod. Th. & Dynam. Sys
"... tiling dynamical systems Abstract. We investigate uniform ergodic type theorems for additive and subadditive functions on a subshift over a finite alphabet. We show that every strictly ergodic subshift admits a uniform ergodic theorem for Banachspacevalued additive functions. We then give a necessa ..."
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Cited by 34 (17 self)
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tiling dynamical systems Abstract. We investigate uniform ergodic type theorems for additive and subadditive functions on a subshift over a finite alphabet. We show that every strictly ergodic subshift admits a uniform ergodic theorem for Banachspacevalued additive functions. We then give a
Ergodic Theorems for Stochastic Operators and Discrete Event Networks
, 1995
"... We present a survey of the main ergodic theory techniques which are used in the study of iterates of monotone and homogeneous stochastic operators. It is shown that ergodic theorems on discrete event networks (queueing networks and/or Petri nets) are a generalization of these stochastic operator the ..."
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Cited by 14 (2 self)
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theorems. Kingman's subadditive ergodic Theorem is the key tool for deriving what we call rst order ergodic results. We also show how to use backward constructions (also called Loynes schemes in network theory) in order to obtain second order ergodic results. We will propose a review of systems
The shape theorem for routelengths in connected spatial networks on random points
, 911
"... For a connected network on Poisson points in the plane, consider the routelength D(r, θ) between a point near the origin and a point near polar coordinates (r, θ), and suppose ED(r, θ) = O(r) as r →∞. By analogy with the shape theorem for firstpassage percolation, for a translationinvariant and ..."
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Cited by 5 (4 self)
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invariant and ergodic network one expects r−1D(r, θ) to converge as r → ∞ to a constant ρ(θ). It turns out there are some subtleties in making a precise formulation and a proof. We give one formulation and proof via a variant of the subadditive ergodic theorem wherein random variables are sometimes infinite. MSC 2000
Results 1  10
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