An upper bound for $p_c$ in range-$R$ bond percolation in two and three dimensions
| Autor: | Hong, Jieliang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | An upper bound for the critical probability of long range bond percolation in $d=2$ and $d=3$ is obtained by connecting the bond percolation with the SIR epidemic model, thus complementing the lower bound result in Frei and Perkins arXiv:arch-ive/1603.04130. A key ingredient is that we establish a uniform bound for the local times of branching random walk by calculating their exponential moments and by using the discrete versions of Tanaka's formula and Garsia's Lemma. |
| Databáze: | arXiv |
| Externí odkaz: |
|