Speaker
Pieter Trapman
(Stockholm University)
Description
The hierarchical lattice of order N, may be seen as the leaves
of an infinite regular N-tree, in which the distance between two
vertices is the distance to their most recent common
ancestor in the tree.
We create a random graph by independent long-range percolation on the hierarchical lattice of order N: The probability that a pair of vertices at (hierarchical) distance R share an edge depends only on R and is exponentially decaying in R, furthermore the presence or absence of different edges are independent.
We give criteria for percolation (the presence of an infinite cluster) and we show that in the supercritical parameter domain, the infinite component is unique. Furthermore, we show the percolation probability (the density of the infinite cluster) is continuous in the model parameters, in particular, there is no percolation at criticality.
Joint work with Slavik Koval and Ronald Meester
We create a random graph by independent long-range percolation on the hierarchical lattice of order N: The probability that a pair of vertices at (hierarchical) distance R share an edge depends only on R and is exponentially decaying in R, furthermore the presence or absence of different edges are independent.
We give criteria for percolation (the presence of an infinite cluster) and we show that in the supercritical parameter domain, the infinite component is unique. Furthermore, we show the percolation probability (the density of the infinite cluster) is continuous in the model parameters, in particular, there is no percolation at criticality.
Joint work with Slavik Koval and Ronald Meester
