Graph constructions for the contact process with a prescribed critical rate

Stein Andreas Bethuelsen; Gabriel Baptista da Silva; Daniel Valesin

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arXiv · 2005.00420

Graph constructions for the contact process with a prescribed critical rate

Stein Andreas Bethuelsen·Gabriel Baptista da Silva·Daniel Valesin

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Abstract

We construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $\lambda_c(\mathbb{Z})$, the critical rate of the one-dimensional contact process. We exhibit both graphs in which the process at this target critical value survives (locally) and graphs where it dies out (globally).

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Stein Andreas Bethuelsen, Gabriel Baptista da Silva, Daniel Valesin. 2020-05-01. Graph constructions for the contact process with a prescribed critical rate. https://arxiv.org/abs/2005.00420

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