4 papers · 1 filter
Gap at 1 for the percolation threshold of Cayley graphs
Christoforos Panagiotis, Franco Severo
We prove that the set of possible values for the percolation threshold of Cayley graphs has a gap at 1 in the sense that there exists such that for every Ca…
On the exponential growth rates of lattice animals and interfaces II: new asymptotic bounds
Agelos Georgakopoulos, Christoforos Panagiotis
We introduce a method for translating any upper bound on the percolation threshold of a lattice into a lower bound on the exponential growth rate of lattice animals and…
Hyperbolic self avoiding walk
Itai Benjamini, Christoforos Panagiotis
Expected ballisticity of a continuous self avoiding walk on hyperbolic spaces is established.
Convergence of square tilings to the Riemann map
Agelos Georgakopoulos, Christoforos Panagiotis
A well-known theorem of Rodin \& Sullivan, previously conjectured by Thurston, states that the circle packing of the intersection of a lattice with a simply connected planar domain…