تقرير
Critical speeding-up in dynamical percolation
| العنوان: | Critical speeding-up in dynamical percolation |
|---|---|
| المؤلفون: | Elci, Eren Metin, Garoni, Timothy M. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Probability, Condensed Matter - Statistical Mechanics, Mathematical Physics |
| الوصف: | We study the autocorrelation time of the size of the cluster at the origin in discrete-time dynamical percolation. We focus on binary trees and high-dimensional tori, and show in both cases that this autocorrelation time is linear in the volume in the subcritical regime, but strictly sublinear in the volume at criticality. This establishes rigorously that the cluster size at the origin in these models exhibits critical speeding-up. The proofs involve controlling relevant Fourier coefficients. In the case of binary trees, these Fourier coefficients are studied explicitly, while for high-dimensional tori we employ a randomised algorithm argument introduced by Schramm and Steif in the context of noise sensitivity. Comment: 28 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.08927 |
| رقم الأكسشن: | edsarx.2402.08927 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |