Abstract
In this paper a new proof of an identity of Giacomin, Olla, and Spohn is given. The identity relates 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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Conlon, J.G. PDE with Random Coefficients and Euclidean Field Theory. Journal of Statistical Physics 116, 933–958 (2004). https://doi.org/10.1023/B:JOSS.0000037204.93858.f2
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DOI: https://doi.org/10.1023/B:JOSS.0000037204.93858.f2