An Optimal Algorithm to Generate Extendable Self-Avoiding Walks in Arbitrary Dimension

Abstract : A self-avoiding walk (SAW) is extendable [10,13] if it can be extended into an infinite SAW. We give a simple proof that, for every lattice, extendable SAWs admit the same connective constant that the general SAWs and we give an optimal linear algorithm to generate random extendable SAWs. Our algorithm can generate every extendable SAW in dimension 2. For dimension d > 2, it generates only a subset of the extendable SAWs. We conjecture that this subset is " large " and has the same connective constant that the extendable SAWs. Our algorithm produces a kinetic distribution of the extendable SAWs, for which the critical exponent ν ≈ .57 for d = 2, .51 for d = 3 and .50 for d = 4, 5, 6.
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Pascal Préa, Mathieu Rouault, François Brucker. An Optimal Algorithm to Generate Extendable Self-Avoiding Walks in Arbitrary Dimension. Electronic Notes in Discrete Mathematics, Elsevier, 2017. ⟨hal-01790908⟩

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