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arXiv · 1706.07495

Dimensional Crossover in Anisotropic Percolation on $Z^{d+s}$

Rémy Sanchis·Roger W. C. Silva
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Abstract

We consider bond percolation on $\Z^d\times \Z^s$ where edges of $\Z^d$ are open with probability $p<p_c(\Z^d)$ and edges of $\Z^s$ are open with probability $q$, independently of all others. We obtain bounds for the critical curve in $(p, q)$, with $p$ close to the critical threshold $p_c(\Z^d)$. The results are related to the so-called dimensional crossover from $\Z^d$ to $\Z^{d+s}$.

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Rémy Sanchis, Roger W. C. Silva. 2017-06-22. Dimensional Crossover in Anisotropic Percolation on $Z^{d+s}$. https://doi.org/10.1007/s10955-017-1905-9

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