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

@article{Bertini1998TheTS,
title={The two-dimensional stochastic heat equation: renormalizing a multiplicative noise},
author={Lorenzo Bertini and Nicoletta Cancrini},
journal={Journal of Physics A},
year={1998},
volume={31},
pages={615-622}
}
• Published 16 January 1998
• Mathematics, Physics
• Journal of Physics A
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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