论文标题
RMF可访问性渗透在方向图上
RMF accessibility percolation on oriented graphs
论文作者
论文摘要
可访问性渗透是一种受到进化生物学启发的新型渗透问题：一个称为其适应性的随机数，被分配给图形的每个顶点，然后，如果严格通过它增加了健身，则可以访问图中的路径。在粗糙的Fuji（RMF）模型中，适应性函数在图表上定义为$ω（v）=η（v）+θ\ cdot d（v）$，其中$θ$是一个称为漂移的正数，$ d $是与图形源的距离，$ d $是图形源，$η（v）$是i.i.d。I.I.D。随机变量。在本文中，我们确定在HyperCube上具有RMF可访问性渗透的$θ$和二维晶格$ \ Mathbb {l}^2 $和$ \ Mathbb {l}^2_ 2_ {alt} $。
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 $ω(v)=η(v)+θ\cdot d(v)$, 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 $\mathbb{L}^2$ and $\mathbb{L}^2_{alt}$.
