The two-dimensional stochastic heat equation: renormalizing a multiplicative noise
The two-dimensional stochastic heat equation: renormalizing a multiplicative noise
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二维随机热方程：乘性噪声的重整化
DOI：
10.1088/0305-4470/31/2/019
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
N. Cancrini
中科院分区：
文献类型：
--
作者：
L. Bertini;N. Cancrini
在二维空间中，我们研究了具有随机势的热方程，该势是时空中的白色噪声。我们引入了一个正则化的噪声和证明，通过一个合适的重整化的耦合系数，协方差有一个非平凡的限制时，正则化被删除。极限描述的两体薛定谔算子奇异的相互作用。
We study, in two space dimensions, the heat equation with a random potential that is a white noise in space and time. We introduce a regularization of the noise and prove that, by a suitable renormalization of the coupling coefficient, the covariance has a non-trivial limit when the regularization is removed. The limit is described in terms of a two-body Schrodinger operator with singular interaction.