# BOUNDING THE NUMBER OF SELF-AVOIDING WALKS: HAMMERSLEY-WELSH WITH POLYGON INSERTION

ANNALS OF PROBABILITY, pp. 1644.0-1692.0, 2020.

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Abstract:

Let c(n) = c(n)(d) denote the number of self-avoiding walks of length n starting at the origin in the Euclidean nearest-neighbour lattice Z(d). Let mu, = lim(n) c(n)(1/n) denote the connective constant of Z(d). In 1962, Hammersley and Welsh (Quart. J. Math. Oxford Ser (2) 13 (1962) 108-110) proved that, for each d >= 2, there exists a con...More

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