Fluctuations in the Composite Regime of a Disordered Growth Model
Fluctuations in the Composite Regime of a Disordered Growth Model
复制标题
无序增长模型的复合机制中的波动
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
H. Widom
中科院分区：
文献类型：
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作者：
Janko Gravner;C. Tracy;H. Widom
翻译后摘要：我们继续研究在两个维度的无序界面生长的模型。 界面由一维整数格点上的高度函数给出，并在离散时间内增长：（1）如果左侧的高度较大，则x点上方的高度采用左侧的高度;（2）否则，x点上方的高度以概率px增加1。我们假设px是独立随机选择的，具有共同的分布F，并且初始状态是这样的，即原点远高于其他位置。如果分布F在其右边的尾部足够薄，则存在一个非平凡的复合区域，其中该界面的波动由px的极值统计决定。在淬火的情况下，所述波动是渐近正常的，而在退火的情况下，它们满足适当的极值极限定律。
Abstract: We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one-dimensional integer lattice and grows in discrete time: (1) the height above the site x adopts the height above the site to its left if the latter height is larger, (2) otherwise, the height above x increases by 1 with probability px. We assume that px are chosen independently at random with a common distribution F, and that the initial state is such that the origin is far above the other sites. Provided that the tails of the distribution F at its right edge are sufficiently thin, there exists a nontrivial composite regime in which the fluctuations of this interface are governed by extremal statistics of px. In the quenched case, the said fluctuations are asymptotically normal, while in the annealed case they satisfy the appropriate extremal limit law.