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.

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

CANCRINI, NICOLETTA
1998-01-01

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/19659
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