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5 papers · 2 filters
Distances in random graphs with finite variance degrees
Remco van der Hofstad, Gerard Hooghiemstra, Piet Van Mieghem
In this paper we study a random graph with nodes, where node has degree and are i.i.d. with $\prob(D_j\leq x)=F(x)$. We assume that $1-F(x)\leq c x^…
Infinite canonical super-Brownian motion and scaling limits
Remco van der Hofstad
We construct a measure valued Markov process which we call infinite canonical super-Brownian motion, and which corresponds to the canonical measure of super-Brownian motion conditi…
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…
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 obtained by independently deleting edges with probability . Let be the number of ve…