论文标题
peierls从Toom Contours界定
Peierls bounds from Toom contours
论文作者
论文摘要
对于$ D $维整数晶格上的确定性单调蜂窝自动机，Toom给出了必要的和足够的条件，使全固定点可以在小的随机扰动中稳定。充分性证明是基于复杂的PEIERLS参数。我们提供了此PEIERLS参数的简化版本。我们的主要动机是用内在的随机性确定单调蜂窝自动机的稳定性的开放问题，其中对于不受干扰的进化，在I.I.D中选择了不同时空点处的本地更新规则。根据一些固定法律的时尚。我们应用Toom的PEIERLS参数来证明具有内在随机性的一类细胞自动机的稳定性，并且对于某些确定性细胞自动机的临界参数也有下限。
For deterministic monotone cellular automata on the $d$-dimensional integer lattice, Toom has given necessary and sufficient conditions for the all-one fixed point to be stable against small random perturbations. The proof of sufficiency is based on an intricate Peierls argument. We present a simplified version of this Peierls argument. Our main motivation is the open problem of determining stability of monotone cellular automata with intrinsic randomness, in which for the unperturbed evolution the local update rules at different space-time points are chosen in an i.i.d. fashion according to some fixed law. We apply Toom's Peierls argument to prove stability of a class of cellular automata with intrinsic randomness and also derive lower bounds on the critical parameter for some deterministic cellular automata.
