Using Random Walks to Establish Wavelike Behavior in an FPUT System with Random Coefficients
Analysis of PDEs
2021-04-02 v1
Abstract
We consider a linear Fermi-Pasta-Ulam-Tsingou lattice with random spatially varying material coefficients. Using the methods of stochastic homogenization we show that solutions with long wave initial data converge in an appropriate sense to solutions of a wave equation. The convergence is strong and both almost sure and in expectation, but the rate is quite slow. The technique combines energy estimates with powerful classical results about random walks, specifically the law of the iterated logarithm.
Cite
@article{arxiv.2104.00463,
title = {Using Random Walks to Establish Wavelike Behavior in an FPUT System with Random Coefficients},
author = {Joshua A. McGinnis and J. Douglas Wright},
journal= {arXiv preprint arXiv:2104.00463},
year = {2021}
}
Comments
26 pages, 5 figures, submitted to DCDS-S