Regensburg 2013 – scientific programme

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BP: Fachverband Biologische Physik

BP 31: Statistical Physics in Biological Systems III (joint with DY)

BP 31.2: Talk

Thursday, March 14, 2013, 15:15–15:30, H46

On the existence of accessible paths in trees — •Stefan Nowak and Joachim Krug — Institute for Theoretical Physics, University of Cologne

The study of accessible paths is a new type of percolation problem which is inspired by evolutionary biology. To each node of the underlying graph a random number is assigned and a path through the graph is called accessible if all random numbers along the path are in ascending order. We will give an exact expression for the second moment of the number of accessible paths from the root to the leafs in n-trees and an asymptotic expression for the probability that there is at least one accessible path. Furthermore, we will show that there is a percolation threshold if the random variables are Gumbel distributed and a linear drift is added.