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- W3003644644 abstract "The key to our investigation is an improved (and in a sense sharp) understanding of the survival time of the contact process on star graphs. Using these results, we show that for the contact process on Galton-Watson trees, when the offspring distribution (i) is subexponential the critical value for local survival $lambda_2=0$ and (ii) when it is geometric($p$) we have $lambda_2 le C_p$, where the $C_p$ are much smaller than previous estimates. We also study the critical value $lambda_c(n)$ for prolonged persistence on graphs with $n$ vertices generated by the configuration model. In the case of power law and stretched exponential distributions where it is known $lambda_c(n) to 0$ we give estimates on the rate of convergence. Physicists tell us that $lambda_c(n) sim 1/Lambda(n)$ where $Lambda(n)$ is the maximum eigenvalue of the adjacency matrix. Our results show that this is not correct." @default.
- W3003644644 created "2020-02-07" @default.
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- W3003644644 date "2020-01-01" @default.
- W3003644644 modified "2023-09-25" @default.
- W3003644644 title "The Contact Process on Random Graphs and Galton Watson Trees" @default.
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- W3003644644 doi "https://doi.org/10.30757/alea.v17-07" @default.
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