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Critical value for contact processes on clusters of oriented bond percolation

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  • Xue, Xiaofeng

Abstract

In this paper we are concerned with contact processes on open clusters of oriented bond percolation in Zd, where the disease spreads along the direction of open edges. We show that the two critical values in the quenched and annealed cases are equal with probability one and are asymptotically equal to (dp)−1 as the dimension d grows to infinity, where p is the probability that the edge is ‘open’.

Suggested Citation

  • Xue, Xiaofeng, 2016. "Critical value for contact processes on clusters of oriented bond percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 205-215.
    • Handle: RePEc:eee:phsmap:v:448:y:2016:i:c:p:205-215
    DOI: 10.1016/j.physa.2015.12.101
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    References listed on IDEAS

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    1. Wang, Jia-zeng & Liu, Zeng-rong & Xu, Jianhua, 2007. "Epidemic spreading on uncorrelated heterogenous networks with non-uniform transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 715-721.
    2. Peterson, Jonathon, 2011. "The contact process on the complete graph with random vertex-dependent infection rates," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 609-629, March.
    3. Xue, Xiaofeng, 2013. "Contact processes with random connection weights on regular graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4749-4759.
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    Cited by:

    1. Xue, Xiaofeng, 2017. "Law of large numbers for the SIR model with random vertex weights on Erdős–Rényi graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 434-445.
    2. Xiaofeng Xue, 2018. "Asymptotic of the Critical Value of the Large-Dimensional SIR Epidemic on Clusters," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2343-2365, December.
    3. Xue, Xiaofeng, 2016. "Critical value for the contact process with random recovery rates and edge weights on regular tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 793-806.

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