An invariance principle for the stochastic heat equation
An invariance principle for the stochastic heat equation
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DOI：
10.1007/s40072-018-0118-9
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发表时间：
2018-05
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影响因子：
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通讯作者：
Mathew Joseph
中科院分区：
文献类型：
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作者：
Mathew Joseph
我们近似白噪声驱动的随机热方程，通过在一维晶格上用离散时间随机游走的生成器代替分数阶拉普拉斯方程，并通过一组i.i.d平均零随机变量逼近白噪声。因此，我们给出了在中间无序状态下定向聚合物的标度配分函数对随机热方程弱收敛性的另一种证明；这个证明的一个优点是它给出了所有矩的收敛性。
We approximate the white-noise driven stochastic heat equation by replacing the fractional Laplacian by the generator of a discrete time random walk on the one dimensional lattice, and approximating white noise by a collection of i.i.d. mean zero random variables. As a consequence, we give an alternative proof of the weak convergence of the scaled partition function of directed polymers in the intermediate disorder regime, to the stochastic heat equation; an advantage of the proof is that it gives the convergence of all moments.