利用随机游动建立具有随机系数的FPUT系统的类波行为
Using Random Walks to Establish Wavelike Behavior in an FPUT System with Random Coefficients
摘要：
本文考虑了材料系数随空间变化的线性Fermi-Pasta-Ulam-Tsingou晶格。利用随机均匀化方法，我们证明了长波初值解在适当的意义下收敛于波动方程的解。收敛是强的，几乎必然和预期的，但速度相当慢。该技术结合了能量估计与强大的经典结果随机游动，特别是法律的重对数。
英文摘要：
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.
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