Critical value for the contact process with random recovery rates and edge weights on regular tree

Xiaofeng Xue

Physica A: Statistical Mechanics and its Applications, 2016, vol. 462, issue C, 793-806

Abstract: In this paper we are concerned with contact processes with random recovery rates and edge weights on rooted regular trees TN. Let ρ and ξ be two nonnegative random variables such that P(ϵ≤ξ<+∞,ρ≤M)=1 for some ϵ,M>0. For each vertex x on TN, ξ(x) is an independent copy of ξ while for each edge e on TN, ρ(e) is an independent copy of ρ. An infected vertex x becomes healthy at rate ξ(x) while an infected vertex y infects an healthy neighbor z at rate proportional to ρ(y,z). For this model, we prove that the critical value under the annealed measure approximately equals (NEρE1ξ)−1 as N grows to infinity. Furthermore, we show that the critical value under the quenched measure equals that under the annealed measure when the cluster containing the root formed with edges with positive weights is infinite.

Keywords: Contact process; Regular tree; Edge weight; Recovery rate; Critical value (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437116302692
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:462:y:2016:i:c:p:793-806

DOI: 10.1016/j.physa.2016.06.001

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().