2016/12/19 by Andrey Piatnitski, Е. Г. Жижина, Elena Zhizhina · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #Continuous-time random walk #Convergence of random variables #Geometry #Heterogeneous random walk in one dimension #Homogenization (climate) #Limit (mathematics) #Loop-erased random walk #Markov chain #Markov process #Mathematical analysis #Mathematics #Physics #Random variable #Random walk #Scaling #Scaling limit #Statistical physics #Statistics #Stochastic process #math-ph #math.MP #math.PR #msc:60J27 #msc:60J35
paper · pdf · doi:10.1007/s10955-017-1883-y
arxiv created 2016/12/19 · openalex publication_date 2017/09/23 · openalex created_date 2017/10/06 · arxiv updated 2017/10/25 · openalex updated_date 2026/08/05
The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in \mathbb Zd, d≥ 1. We show that under proper diffusive scaling the random walk exhibits a non-standard limit behaviour. In addition to the coordinate of the random walk in \mathbb Zd we introduce an extra variable that characterizes the position of the random walk in the period and show that this two-component process converges in law to a limit Markov process. The components of the limit process are mutually coupled, thus we cannot expect that the limit behaviour of the coordinate process is Markov. We also prove the convergence in the path space for the said random walk.