Approximation of subadditive functions and convergence rates in limiting-shape results
Approximation of subadditive functions and convergence rates in limiting-shape results
复制标题
极限形状结果中次加性函数和收敛速度的近似
DOI：
10.1214/aop/1024404277
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发表时间：
1997
影响因子：
2.3
通讯作者：
K. S. Alexander
中科院分区：
文献类型：
--
作者：
K. S. Alexander
对于Zd上的非负次可加函数h，在极限逼近g（x）= lim nh（nx）/n下，得到g（x）和h（x）之间的偏差的界是很有意义的，一般为|X|其中v < 1。对于某些次可加h（x），特别是那些与从0到x的最优随机路径相关的期望，可以以某种标准化的方式建立一个更自然和似乎更弱的性质：每个x都在满足类似界限的点集的凸船体的有界倍数中。我们表明，这种凸壳属性意味着所有x的期望的范围。应用程序包括收敛速度的限制形状的结果，第一次通过渗流（标准和定向）和最长的共同concierences和边界上的错误，在指数衰减近似的离轴连接功能的亚临界伯努利债券渗流整数格。
For a nonnegative subadditive function h on Z d , with limiting approximation g(x) = lim n h(nx)/n, it is of interest to obtain bounds on the discrepancy between g(x) and h(x), typically of order |x| with ν < 1. For certain subadditive h(x), particularly those which are expectations associated with optimal random paths from 0 to x, in a somewhat standardized way a more natural and seemingly weaker property can be established: every x is in a bounded multiple of the convex hull of the set of sites satisfying a similar bound. We show that this convex-hull property implies the desired bound for all x. Applications include rates of convergence in limiting-shape results for first-passage percolation (standard and oriented) and longest common subsequences and bounds on the error in the exponential-decay approximation to the off-axis connectivity function for subcritical Bernoulli bond percolation on the integer lattice.