This paper is dedicated to the memory of Dietrich Stauffer, who was a pioneer in percolation
theory and applications of it to problems of society, such as epidemiology. An epidemic is a …

The gel point of end-linked model networks is determined from computer simulation data. It
is shown that the difference between the true gel point conversion, pc, and the ideal mean …

Extended-range percolation on various regular lattices, including all 11 Archimedean
lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face …

By means of extensive Monte Carlo simulation, we study extended-range site percolation on
square and simple cubic lattices with various combinations of nearest neighbors up to the …

Classical percolation theory underlies many processes of information transfer along the links
of a network. In these standard situations, the requirement for two nodes to be able to …

Exact or precise thresholds have been intensively studied since the introduction of the
percolation model. Recently, the critical polynomial PB (p, L) was introduced for planar …

In dimensions $ d\geq 4$, by choosing a suitable scaling parameter, we show that the
rescaled spatial SIR epidemic process converges to a super-Brownian motion with drift, thus …

Percolation on a five-dimensional simple hypercubic (sc (5)) lattice with extended
neighborhoods is investigated by means of extensive Monte Carlo simulations, using an …

An upper bound for the critical probability of the range-R bond percolation in d= 2 and d= 3
is obtained by connecting the bond percolation with the SIR epidemic model, thus …

The asymptotic behavior of the percolation threshold pc and its dependence upon
coordination number z is investigated for both site and bond percolation on four-dimensional …