212 citations · 1.1k across the 33 of their papers we have counts for
35 papers
Astronomia Ova: Kepler's Laws, Ptolemy's Equant, and Legendre's Polynomials
Cristopher Moore, Malcolm Smith, Stephan Mertens
Motivated by Kepler's long battle with the orbit of Mars, we present a family of orbits that satisfy his second law, conserving angular momentum around a central mass, and also ful…
Exact Percolation Probability on the Square Lattice
Stephan Mertens
We present an algorithm to compute the exact probability for a site percolation cluster to span an square lattice at occupancy . The algorithm has time an…
Percolation is Odd
Stephan Mertens, Cristopher Moore
We prove a remarkable combinatorial symmetry in the number of spanning configurations in site percolation: for a large class of lattices, the number of spanning configurations with…
Percolation Thresholds and Fisher Exponents in Hypercubic Lattices
Stephan Mertens, Cristopher Moore
We use invasion percolation to compute highly-accurate numerical values for bond and site percolation thresholds p_c on the hypercubic lattice Z^d for d = 4,,,,,13. We also compute…
Series Expansion of the Percolation Threshold on Hypercubic Lattices
Stephan Mertens, Cristopher Moore
We study proper lattice animals for bond- and site-percolation on the hypercubic lattice to derive asymptotic series of the percolation threshold in , The…
Percolation Thresholds in Hyperbolic Lattices
Stephan Mertens, Cristopher Moore
We use invasion percolation to compute numerical values for bond and site percolation thresholds (existence of an infinite cluster) and (uniqueness of the infinite clus…