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• W3034352455 abstract "Associated to any finite simple graph Γ is the chromatic polynomial PΓ(q) whose complex zeros are called the chromatic zeros of Γ. A hierarchical lattice is a sequence of finite simple graphs {Γn}∞n-0 built recursively using a substitution rule expressed in terms of a generating graph. For each n, let μn denote the probability measure that assigns a Dirac measure to each chromatic zero of Γn. Under a mild hypothesis on the generating graph, we prove that the sequence μn converges to some measure μ as n tends to infinity. We call μ the limiting measure of chromatic zeros associated to {Γn}∞n-0. In the case of the Diamond Hierarchical Lattice we prove that the support of μ has Hausdorff dimension two.The main techniques used come from holomorphic dynamics and more specifically the theories of activity/bifurcation currents and arithmetic dynamics. We prove anew equidistribution theorem that can be used to relate the chromatic zeros of ahierarchical lattice to the activity current of a particular marked point. We expect that this equidistribution theorem will have several other applications, and describe one such example in statistical mechanics about the Lee-Yang-Fisher zeros for the Cayley Tree." @default.
• W3034352455 created "2020-06-19" @default.
• W3034352455 creator A5050331732 @default.
• W3034352455 date "2020-06-15" @default.
• W3034352455 modified "2023-10-16" @default.
• W3034352455 title "Some Connections Between Complex Dynamics and Statistical Mechanics" @default.
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• W3034352455 doi "https://doi.org/10.25394/pgs.12331136.v1" @default.
• W3034352455 hasPublicationYear "2020" @default.
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