3 citations · 5 across the 3 of their papers we have counts for
5 papers · 1 filter
Asymptotic expansions in for percolation critical values on the -cube and
Remco van der Hofstad, Gordon Slade
We use the lace expansion to prove that the critical values for nearest-neighbour bond percolation on the -cube and on have asymptotic expansions, wit…
Random subgraphs of finite graphs: III. The phase transition for the -cube
Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad +2
We study random subgraphs of the -cube , where nearest-neighbor edges are occupied with probability . Let be the value of for which the expected clust…
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…
A generalised inductive approach to the lace expansion
Remco van der Hofstad, Gordon Slade
The lace expansion is a powerful tool for analysing the critical behaviour of self-avoiding walks and percolation. It gives rise to a recursion relation which we abstract and study…
Lattice trees, percolation and super-Brownian motion
Gordon Slade
This paper surveys the results of recent collaborations with Eric Derbez and with Takashi Hara, which show that intergrated super-Brownian excursion (ISE) arises as the scaling lim…