03-35 Joseph G. Conlon

PDE with Random Coefficients and Euclidean Field Theory} (285K, postscript) Feb 3, 03

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Abstract. In this paper an identity is proved relating the 2 point correlation function of a Euclidean field theory to the expectation of the Green's function for a pde with random coefficients. The Euclidean field theory is assumed to have convex potential. An inequality of Brascamp and Lieb therefore implies Gaussian bounds on the Fourier transform of the 2 point correlation function. By an application of results from random pde, the previously mentioned identity implies pointwise Gaussian bounds on the 2 point correlation function.

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