First contact percolation
Authors
- Jahnel, Benedikt
ORCID: 0000-0002-4212-0065 - Lüchtrath, Lukas
ORCID: 0000-0003-4969-806X - Vu, Anh Duc
ORCID: 0009-0005-6913-4992
2020 Mathematics Subject Classification
- 60K05 60K35 82B43
Keywords
- First passage percolation, contact process, pure-growth process, shape theorem
DOI
Abstract
We study a version of first passage percolation on Zd where the random passage times on the edges are replaced by contact times represented by random closed sets on R. Similarly to the contact process without recovery, an infection can spread into the system along increasing sequences of contact times. In case of stationary contact times, we can identify associated first passage percolation models, which in turn establish shape theorems also for first contact percolation. In case of periodic contact times that reflect some reoccurring daily pattern, we also present shape theorems with limiting shapes that are universal with respect to the within-one-day contact distribution. In this case, we also prove a Poisson approximation for increasing numbers of within-one-day contacts. Finally, we present a comparison of the limiting speeds of three models -- all calibrated to have one expected contact per day -- that suggests that less randomness is beneficial for the speed of the infection. The proofs rest on coupling and subergodicity arguments.
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