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Asymptotic behavior of two-terminal series-parallel networks

O. Golinelli
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Abstract

This paper discusses the enumeration of two-terminal series-parallel networks, i.e. the number of electrical networks built with n identical elements connected in series or parallel with two-terminal nodes. They frequently occur in applied probability theory as a model for real networks. The number of networks grows asymptotically like R^n/n^alpha, as for some models of statistical physics like self-avoiding walks, lattice animals, meanders, etc. By using a exact recurrence relation, the entropy is numerically estimated at R = 3.5608393095389433(1), and we show that the sub-leading universal exponent alpha is 3/2.

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O. Golinelli. 1997-07-02. Asymptotic behavior of two-terminal series-parallel networks. https://arxiv.org/abs/cond-mat/9707023

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