Gaussian deconvolution and the lace expansion for spread-out models

2023/10/11 by Liu, Yucheng, Slade, Gordon · 1 citation
#42B05 #60K35 #82B27 #82B41 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2310.07640

Abstract

We present a new proof of |x|^-(d-2) decay of critical two-point functions for spread-out statistical mechanical models on ℤ^d above the upper critical dimension, based on the lace expansion and assuming appropriate diagrammatic estimates. Applications include spread-out models of the Ising model and self-avoiding walk in dimensions d>4, and spread-out percolation for d>6. The proof is based on an extension of the new Gaussian deconvolution theorem we obtained in a recent paper. It provides a technically simpler and conceptually more transparent approach than the method of Hara, van der Hofstad and Slade (2003).

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