Author:
Duque Frank,Ramirez-Gomez Daniel,Roldán-Correa Alejandro,Valencia Leon A
Abstract
Abstract
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology: a random number, called its fitness, is assigned to each vertex of a graph, then a path in the graph is accessible if fitnesses are strictly increasing through it. In the rough Mount Fuji (RMF) model, the fitness function is defined on the graph as
ω
(
v
)
=
η
(
v
)
+
θ
⋅
d
(
v
)
, where θ is a positive number called the drift, d is the distance to the source of the graph and
η
(
v
)
are i.i.d. random variables. In this paper, we determine values of θ for having RMF accessibility percolation on the hypercube and the two-dimensional lattices
L
2
and
L
a
l
t
2
.
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Statistical and Nonlinear Physics