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arXiv · 2310.07640

Gaussian deconvolution and the lace expansion for spread-out models

Yucheng Liu·Gordon Slade
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Abstract

We present a new proof of $|x|^{-(d-2)}$ decay of critical two-point functions for spread-out statistical mechanical models on $\mathbb{Z}^d$ 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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Yucheng Liu, Gordon Slade. 2024-05-17. Gaussian deconvolution and the lace expansion for spread-out models. https://doi.org/10.1214/24-aihp1509

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