Gaussian deconvolution and the lace expansion for spread-out models
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914356754644992 |
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| author | Liu, Yucheng Slade, Gordon |
| author_facet | Liu, Yucheng Slade, Gordon |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07640 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gaussian deconvolution and the lace expansion for spread-out models Liu, Yucheng Slade, Gordon Probability Mathematical Physics 42B05, 60K35, 82B27, 82B41, 82B43 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). |
| title | Gaussian deconvolution and the lace expansion for spread-out models |
| topic | Probability Mathematical Physics 42B05, 60K35, 82B27, 82B41, 82B43 |
| url | https://arxiv.org/abs/2310.07640 |