论文标题
多项式生长图的渗透的局部性
Locality of percolation for graphs with polynomial growth
论文作者
论文摘要
Schramm的当地猜想断言，满足$ P_C <1 $的图的关键渗透参数$ P_C $仅取决于其本地结构。在本说明中，我们在具有多项式生长的特定情况下证明了这种猜想。我们的证明依靠有关此类图的最近作品，即同一作者对渗透的超临界清晰度以及Tessera和Tointon的限制结构定理。
Schramm's Locality Conjecture asserts that the value of the critical percolation parameter $p_c$ of a graph satisfying $p_c<1$ depends only on its local structure. In this note, we prove this conjecture in the particular case of transitive graphs with polynomial growth. Our proof relies on two recent works about such graphs, namely supercritical sharpness of percolation by the same authors and a finitary structure theorem by Tessera and Tointon.
