G. Slade

activity

19982004

most citedRandom subgraphs of finite graphs: III. The phase transition for the

n

-cube

3 citations · 5 across the 3 of their papers we have counts for

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Showing 2004 · math.PRShow all

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math.PR2004★ 2 cited

Asymptotic expansions in $n^{- 1}$ for percolation critical values on the $n$ -cube and $Z^{n}$

Remco van der Hofstad, Gordon Slade

We use the lace expansion to prove that the critical values for nearest-neighbour bond percolation on the $n$ -cube ${0, 1}^{n}$ and on $Z^{n}$ have asymptotic expansions, wit…

math.PR2004★ 3 cited

Random subgraphs of finite graphs: III. The phase transition for the $n$ -cube

Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad +2

We study random subgraphs of the $n$ -cube ${0, 1}^{n}$ , where nearest-neighbor edges are occupied with probability $p$ . Let $p_{c} (n)$ be the value of $p$ for which the expected clust…

math.PR2004

Random subgraphs of finite graphs: II. The lace expansion and the triangle condition

Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad +2

In a previous paper, we defined a version of the percolation triangle condition that is suitable for the analysis of bond percolation on a finite connected transitive graph, and sh…

Asymptotic expansions in n−1 for percolation critical values on the n-cube and Zn

Random subgraphs of finite graphs: III. The phase transition for the n-cube

Random subgraphs of finite graphs: II. The lace expansion and the triangle condition

Asymptotic expansions in $n^{- 1}$ for percolation critical values on the $n$ -cube and $Z^{n}$

Random subgraphs of finite graphs: III. The phase transition for the $n$ -cube