Invariant Gibbs measures for the 2-$d$ defocusing nonlinear wave equations
Invariant Gibbs measures for the 2-$d$ defocusing nonlinear wave equations
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DOI：
10.5802/afst.1620
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发表时间：
2017-03
期刊：
影响因子：
--
通讯作者：
Tadahiro Oh;Laurent Thomann
中科院分区：
文献类型：
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作者：
Tadahiro Oh;Laurent Thomann
考虑二维环面上的散焦非线性波动方程。特别是，我们构造不变的吉布斯措施的重整化所谓的威克有序NLW。然后，我们证明了弱的普遍性的Wick有序NLW，表明Wick有序NLW自然出现作为一个合适的标度极限的非重整化NLW与高斯随机初始数据。
We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick ordered NLW, showing that the Wick ordered NLW naturally appears as a suitable scaling limit of non-renormalized NLW with Gaussian random initial data.