Graph Constructions for the Contact Process with a Prescribed Critical Rate

Stein Andreas Bethuelsen; Gabriel Baptista da Silva; Daniel Valesin

doi:10.1007/s10959-020-01063-4

Graph Constructions for the Contact Process with a Prescribed Critical Rate

Stein Andreas Bethuelsen, Gabriel Baptista da Silva^*, Daniel Valesin

^*Corresponding author for this work

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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 λ_c(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).

Original language	English
Pages (from-to)	863–893
Number of pages	31
Journal	Journal of theoretical probability
Volume	35
Early online date	28-Jan-2021
DOIs	https://doi.org/10.1007/s10959-020-01063-4
Publication status	Published - Jun-2022

Keywords

Contact process
Critical value
Interacting particle systems
Phase transition

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Graph Constructions for the Contact Process with a Prescribed Critical RateFinal publisher's version, 490 KBLicence: CC BY

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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 λc(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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AU - da Silva, Gabriel Baptista

AU - Valesin, Daniel

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N2 - 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 λc(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).

AB - 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 λc(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).

KW - Contact process

KW - Critical value

KW - Interacting particle systems

KW - Phase transition

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ER -

Graph Constructions for the Contact Process with a Prescribed Critical Rate

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