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The continuous-time lace expansion
- Publication Year :
- 2019
-
Abstract
- We derive a continuous-time lace expansion for a broad class of self-interacting continuous-time random walks. Our expansion applies when the self-interaction is a sufficiently nice function of the local time of a continuous-time random walk. As a special case we obtain a continuous-time lace expansion for a class of spin systems that admit continuous-time random walk representations. We apply our lace expansion to the $n$-component $g|\varphi|^4$ model on $\mathbb{Z}^{d}$ when $n=1,2$, and prove that the critical Green's function $G_{\nu_{c}}(x)$ is asymptotically a multiple of $|x|^{2-d}$ when $d\geq 5$ at weak coupling. As another application of our method we establish the analogous result for the lattice Edwards model at weak coupling.<br />Comment: Final version
- Subjects :
- Mathematics - Probability
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1905.09605
- Document Type :
- Working Paper