Rescaled SIR epidemic processes converge to super-Brownian motion in four or more dimensions
| Autor: | Hong, Jieliang |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In dimensions $d\geq 4$, by choosing a suitable scaling parameter, we show that the rescaled spatial SIR epidemic process converges to a super-Brownian motion with drift, thus complementing the previous results by Lalley (Probab. Theory Related Fields,144(2009),429--469) and Lalley-Zheng (Prob. Th. Rel. Fields,148(2010),527--566) on the convergence of SIR epidemics in $d\leq 3$. The scaling parameters we choose also agree with the corresponding asymptotics for the critical probability $p_c$ of the range-$R$ bond percolation on $\mathbb{Z}^d$ as $R\to \infty$. Comment: 80 pages, 4 figures |
| Databáze: | arXiv |
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