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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The first author acknowledges the support of NSF grant DMS-1613261.
The second author acknowledges the support of NSF grant DMS-1500685.
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McGoff, K., Pavlov, R. Factor maps and embeddings for random ℤd shifts of finite type. Isr. J. Math. 230, 239–273 (2019). https://doi.org/10.1007/s11856-018-1822-x
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DOI: https://doi.org/10.1007/s11856-018-1822-x