A PROBABILISTIC MODEL FOR INTERFACES IN A MARTENSITIC PHASE TRANSITION

Pierluigi Cesana, Ben M. Hambly

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1081-1105
Number of pages25
JournalJournal of Applied Probability
Volume59
Issue number4
DOIs
Publication statusPublished - Dec 9 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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