The contact process on periodic trees
A little over 25 years ago Pemantle [6] pioneered the study of the contact process on trees, and showed that on homogeneous trees the critical values ⅄1 and ⅄2 for global and local survival were different. He also considered trees with periodic degree sequences, and Galton-Watson trees. Here, we will consider periodic trees in which the number of children in successive generations is (n, a1,..., ak) with maxiai ≤ Cn1-δand log(a1· · · ak)= log n→b as n→ ꝏ. We show that the critical value for local survival is asymptotically √c(log)/n where c = (k ̶ b)/2. This supports Pemantle’s claim that the critical value is largely determined by the maximum degree, but it also shows that the smaller degrees can make a significant contribution to the answer.
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- 0104 Statistics
Citation
Published In
DOI
EISSN
Publication Date
Volume
Related Subject Headings
- Statistics & Probability
- 0104 Statistics