Heavy tails in last-passage percolation
Heavy tails in last-passage percolation
复制标题
最后一段渗透中出现重尾
DOI：
10.1007/s00440-006-0019-0
复制
发表时间：
2006
影响因子：
2
通讯作者：
James B. Martin
中科院分区：
文献类型：
--
作者：
B. Hambly;James B. Martin
我们考虑二维的最后通道渗透模型，其中基础权重分布具有索引 α < 2 的重尾。我们证明了通道时间和最佳路径形状的缩放定律和渐近分布；这些以单位平方中的“连续最后通道渗滤”模型族（由 α 索引）来表示。在极端情况下 α = 0（对应于尾部缓慢变化的分布），最优路径的渐近分布可以由 [0,1] 上的随机自相似测度表示，我们计算其多重分形谱。通过扩展连续的最后通道渗透模型，我们获得了艾里过程的重尾模拟，代表了平面上不同点的适当缩放的通道时间向量的极限。我们给出了基于 α-稳定 Lévy 过程的定向渗流问题的相应结果，并将结果扩展到更高维度。
We consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index α < 2. We prove scaling laws and asymptotic distributions, both for the passage times and for the shape of optimal paths; these are expressed in terms of a family (indexed by α) of “continuous last-passage percolation” models in the unit square. In the extreme case α = 0 (corresponding to a distribution with slowly varying tail) the asymptotic distribution of the optimal path can be represented by a random self-similar measure on [0,1], whose multifractal spectrum we compute. By extending the continuous last-passage percolation model towe obtain a heavy-tailed analogue of the Airy process, representing the limit of appropriately scaled vectors of passage times to different points in the plane. We give corresponding results for a directed percolation problem based on α-stable Lévy processes, and indicate extensions of the results to higher dimensions.
随机矩阵和非碰撞过程。
DOI：
--
发表时间：
2006
期刊：
Invitation to Mathematical Physics(Yuusei-sha) 28
影响因子：
--
作者：
M.Kokubu;M.Umehara;K.Yamada;Makoto Katori
通讯作者：
Makoto Katori