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 voor dit werk

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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).

Originele taal-2	English
Pagina's (van-tot)	863–893
Aantal pagina's	31
Tijdschrift	Journal of theoretical probability
Volume	35
Vroegere onlinedatum	28-jan.-2021
DOI's	https://doi.org/10.1007/s10959-020-01063-4
Status	Published - jun.-2022

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10.1007/s10959-020-01063-4Licentie: CC BY

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

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AU - da Silva, Gabriel Baptista

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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).

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KW - Phase transition

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Graph Constructions for the Contact Process with a Prescribed Critical Rate

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