The two-dimensional stochastic heat equation: renormalizing a multiplicative noise

被引：29
|
作者：
Bertini, L
Cancrini, N
机构：
[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2BZ, England
[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[3] Ecole Polytech, Ctr Phys Theor, F-91128 Palaiseau, France
[4] Univ Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italy
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1998年 / 31卷 / 02期
关键词：
D O I：
10.1088/0305-4470/31/2/019
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
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页码：615 / 622
页数：8
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