论文标题
在第一分渗透中的存在和共存
Existence and coexistence in first-passage percolation
论文作者
论文摘要
我们认为与I.I.D.在瞬间条件下，非负重来自一些连续分布。我们回顾了在第一学期渗透中测量学研究的最新结果，并研究了它们对多类理查森模型的影响。在二维中，这建立了无限大地测量学的存在与竞争类型之间的共存之间的双重关系。该论点构成确切的启发式方法，即无限的大地测量学可以被视为“通往无限的高速公路”。我们通过在高于两个的维度中呈现部分结果来解释当前技术的局限性。
We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of geodesics in first-passage percolation and study their implications for the multi-type Richardson model. In two dimensions this establishes a dual relation between the existence of infinite geodesics and coexistence among competing types. The argument amounts to making precise the heuristic that infinite geodesics can be thought of as `highways to infinity'. We explain the limitations of the current techniques by presenting a partial result in dimensions higher than two.
