01-398 Gastao A. Braga, Aldo Procacci, Remy Sanchis

Analyticity of the d-dimensional bond percolation probability around p=1 (501K, PostScript) Oct 25, 01

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Abstract. Let $\theta(p)$ be the percolation probability of a $d$-dimensional bond percolation process on $Z^d$. \\We prove that $1-\theta(p)$ can be written as an absolutely convergent series in powers of $(1-p)/p$, provided that $|(1-p)/p|$ is sufficiently small. This implies that $\theta(p)$ is an analytic function of the complex variable $p$, around $p=1$.

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