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- W2080494101 abstract "Let $$Z_N$$ be the number of self-avoiding paths of length $$N$$ starting from the origin on the infinite cluster obtained after performing Bernoulli percolation on $${mathbb Z} ^d$$ with parameter $$p>p_c({mathbb Z} ^d)$$ . The object of this paper is to study the connective constant of the dilute lattice $$limsup _{Nrightarrow infty } Z_N^{1/N}$$ , which is a non-random quantity. We want to investigate if the inequality $$limsup _{Nrightarrow infty } (Z_N)^{1/N} le lim _{Nrightarrow infty } {mathbb E} [Z_N]^{1/N}$$ obtained with the Borel–Cantelli Lemma is strict or not. In other words, we want to know if the quenched and annealed versions of the connective constant are equal. On a heuristic level, this indicates whether or not localization of the trajectories occurs. We prove that when $$d$$ is sufficiently large there exists $$p^{(2)}_c>p_c$$ such that the inequality is strict for $$pin (p_c,p^{(2)}_c)$$ ." @default.
- W2080494101 created "2016-06-24" @default.
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- W2080494101 date "2014-02-08" @default.
- W2080494101 modified "2023-09-27" @default.
- W2080494101 title "Existence of a Non-Averaging Regime for the Self-Avoiding Walk on a High-Dimensional Infinite Percolation Cluster" @default.
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- W2080494101 doi "https://doi.org/10.1007/s10955-014-0926-x" @default.
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