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Factor maps and embeddings for random ℤd Shifts of Finite Type

  • Kevin McGoff
  • Ronnie PavlovEmail author
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Abstract

For any d ≥ 1, random ℤd shifts of finite type (SFTs) were defined in previous work of the authors. For a parameter α ∈ [0, 1], an alphabet \(\mathcal{A}\), and a scale n ∈ ℕ, one obtains a distribution of random ℤd SFTs by randomly and independently forbidding each pattern of shape {1,..., n}d with probability 1−α from the full shift on \(\mathcal{A}\). We prove twomain results concerning random ℤd SFTs. First, we establish sufficient conditions on α, \(\mathcal{A}\), and a ℤd subshift Y so that a random ℤd SFT factors onto Y with probability tending to one as n tends to infinity. Second, we provide sufficient conditions on α, \(\mathcal{A}\) and a ℤd subshift X so that X embeds into a random ℤd SFT with probability tending to one as n tends to infinity.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North Carolina at CharlotteCharlotteUSA
  2. 2.Department of MathematicsUniversity of DenverDenverUSA

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