RMF accessibility percolation on oriented graphs

Abstract Accessibility percolation is a new type of problem inspired by evolutionary biology: random number, called its fitness, assigned to each vertex graph, then path in the graph accessible if fitnesses are strictly increasing through it. In rough Mount Fuji (RMF) model, fitness function defined on as ω ( v stretchy="false">) = η + θ ⋅ d , where θ positive number drift, d distance source and $\eta(v)$?> i.i.d. variables. this paper, we determine values for having RMF accessibility hypercube two-dimensional lattices $\mathbb{L}^2$?> L 2 $\mathbb{L}^2_{alt}$?> a l t .