2018
DOI: 10.1090/conm/719/14471
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Eternal Family Trees and dynamics on unimodular random graphs

Abstract: This paper is centered on covariant dynamics on unimodular random graphs and random networks (marked graphs), namely maps from the set of vertices to itself which are preserved by graph or network isomorphisms. Such dynamics are referred to as vertex-shifts here.The first result of the paper is a classification of vertex-shifts on unimodular random networks. Each such vertex-shift partitions the vertices into a collection of connected components and foils. The latter are discrete analogues the stable manifold … Show more

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Cited by 14 publications
(27 citation statements)
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“…The Φ-graph of Γ is the graph drawn on Γ with vertices V (Γ) and edges from each v ∈ V (Γ) to Φ Γ (v). The following is a special case of the classification theorem appearing in [2]. Theorem 3.1 (Foil Classification in Unimodular Networks [2]).…”
Section: Definition and Basic Propertiesmentioning
confidence: 99%
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“…The Φ-graph of Γ is the graph drawn on Γ with vertices V (Γ) and edges from each v ∈ V (Γ) to Φ Γ (v). The following is a special case of the classification theorem appearing in [2]. Theorem 3.1 (Foil Classification in Unimodular Networks [2]).…”
Section: Definition and Basic Propertiesmentioning
confidence: 99%
“…The following is a special case of the classification theorem appearing in [2]. Theorem 3.1 (Foil Classification in Unimodular Networks [2]). Let [Γ, o] be a unimodular network and Φ a vertex-shift.…”
Section: Definition and Basic Propertiesmentioning
confidence: 99%
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