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}
}
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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