A lower bound for $p_c$ in range-$R$ bond percolation in two and three dimensions
| Autor: | Spencer Frei, Edwin Perkins |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
long range bond percolation 60J80 Bond Probability (math.PR) 01 natural sciences Upper and lower bounds 60K35 (Primary) 60J68 60J80 92D30 (Secondary) 010305 fluids & plasmas Connection (mathematics) Combinatorics SIR epidemic 60K35 Percolation 0103 physical sciences 92D30 FOS: Mathematics Range (statistics) 60J68 Statistics Probability and Uncertainty critical probability 010306 general physics Critical probability Mathematics - Probability Mathematics |
| Zdroj: | Electron. J. Probab. |
| Popis: | We use the connection between bond percolation and SIR epidemics to establish lower bounds for the critical percolation probability in $2$ and $3$ dimensions as the range becomes large. The bound agrees with the conjectured asymptotics for the long range critical probability, refines results of M. Penrose, and complements results of van der Hofstad and Sakai in dimensions greater than $6$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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