A probabilistic model for interfaces in a martensitic phase transition
A probabilistic model for interfaces in a martensitic phase transition
复制标题
马氏体相变界面的概率模型
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
B. Hambly
中科院分区：
文献类型：
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作者：
Pierluigi Cesana;B. Hambly
摘要：我们分析了马氏体相变的一个简单模型所形成的图案的特征，该模型将单位正方形分割成矩形。这是一个碎片模型，可以用一般的分支随机漫步来编码。一个重要的量是界面长度在模式中的分布，并且我们建立了一些界面轮廓渐近的极限定理。特别是，我们能够使用一般分支过程来显示至少具有一定尺寸的界面数量的几乎确定的幂律衰减，并使用一般分支随机漫步来检查具有一定纵横比的矩形的数量。在此过程中，我们推广了一般分支随机漫步的生长定理，并发展了一般分支过程中极限随机变量尾部行为的结果。
Abstract We analyse features of the patterns formed from a simple model for a martensitic phase transition that fragments the unit square into rectangles. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the lengths of the interfaces in the pattern, and we establish limit theorems for some of the asymptotics of the interface profile. In particular, we are able to use a general branching process to show almost sure power law decay of the number of interfaces of at least a certain size and a general branching random walk to examine the numbers of rectangles of a certain aspect ratio. In doing so we extend a theorem on the growth of the general branching random walk as well as developing results on the tail behaviour of the limiting random variable in our general branching process.