Gaussian scaling for the critical spread-out contact process above the upper critical dimension.
A local limit theorem for the critical random graph.
An extension of the inductive approach to the lace expansion.
Distances in random graphs with finite mean and infinite variance degrees.
Convergence of critical oriented percolation to super-brownian motion above dimensions
Cycle structure of percolation on high-dimensional tori
In the past years, many properties of the largest connected components of critical percolation on the high-dimensional torus, such as their sizes and diameter, have been established. The order of magnitude of these quantities equals the one for percolation on the complete graph or Erdős–Rényi random graph, raising the question whether the scaling limits of the largest connected components, as identified by Aldous (1997), are also equal. In this paper, we investigate the of the largest critical components...
Scale-free percolation
We formulate and study a model for inhomogeneous long-range percolation on . Each vertex is assigned a non-negative weight , where are i.i.d. random variables. Conditionally on the weights, and given two parameters , the edges are independent and the probability that there is an edge between and is given by . The parameter is the percolation parameter, while describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there...
The survival probability for critical spread-out oriented percolation above dimensions. II. Expansion
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