Gordon Slade

most citedRandom subgraphs of finite graphs: I. The scaling window under the triangle condition

89 citations · 98 across the 5 of their papers we have counts for

collaborators

5 papers

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★ 4 cited

Expansion in $n^{- 1}$ for percolation critical values on the $n$ -cube and $Z^{n}$ : the first three terms

Remco van der Hofstad, Gordon Slade

Let $p_{c} (Q_{n})$ and $p_{c} (Z^{n})$ denote the critical values for nearest-neighbour bond percolation on the $n$ -cube $Q_{n} = {0, 1}^{n}$ and on $Z^{n}$ , respecti…

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…

math.PR2004★ 89 cited

Random subgraphs of finite graphs: I. The scaling window under the triangle condition

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

We study random subgraphs of an arbitrary finite connected transitive graph $G$ obtained by independently deleting edges with probability $1 - p$ . Let $V$ be the number of ve…

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

Expansion in n−1 for percolation critical values on the n-cube and Zn: the first three terms

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

Random subgraphs of finite graphs: I. The scaling window under the triangle condition

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

Expansion in $n^{- 1}$ for percolation critical values on the $n$ -cube and $Z^{n}$ : the first three terms

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