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Dual Families of Interacting Particle Systems on Graphs

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  • Aidan Sudbury

    (Monash University)

Abstract

A simple condition for IPS (Interacting Particle Systems) with nearest neighbor interactions to be self-dual is given. It follows that any IPS with the contact transition and no spontaneous birth is self-dual. It is shown that families of IPS exist in which every IPS is dual to every other, and such that for every pair of IPS, one is a “thinning” of the other. Further, all such IPS have the same form for an equilibrium distribution when expressed in terms of survival probabilities. Convergence results from a wide class of initial infinite measures follow.

Suggested Citation

  • Aidan Sudbury, 2000. "Dual Families of Interacting Particle Systems on Graphs," Journal of Theoretical Probability, Springer, vol. 13(3), pages 695-716, July.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:3:d:10.1023_a:1007806427774
    DOI: 10.1023/A:1007806427774
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    References listed on IDEAS

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    1. Belitsky, Vladimir & Ferrari, Pablo A. & Konno, Norio & Liggett, Thomas M., 1997. "A strong correlation inequality for contact processes and oriented percolation," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 213-225, May.
    2. Sudbury, Aidan, 1997. "The convergence of the biased annihilating branching process and the double-flipping process in d," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 255-264, June.
    3. Bramson, Maury & Wan-ding, Ding & Durrett, Rick, 1991. "Annihilating branching processes," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 1-17, February.
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    Cited by:

    1. Anja Sturm & Jan M. Swart, 2018. "Pathwise Duals of Monotone and Additive Markov Processes," Journal of Theoretical Probability, Springer, vol. 31(2), pages 932-983, June.
    2. Makoto Katori & Norio Konno & Aidan Sudbury & Hideki Tanemura, 2004. "Dualities for the Domany–Kinzel Model," Journal of Theoretical Probability, Springer, vol. 17(1), pages 131-144, January.
    3. Jan Niklas Latz & Jan M. Swart, 2023. "Commutative Monoid Duality," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1088-1115, June.

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    1. Jan Niklas Latz & Jan M. Swart, 2023. "Commutative Monoid Duality," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1088-1115, June.
    2. Sudbury, Aidan, 1997. "The convergence of the biased annihilating branching process and the double-flipping process in d," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 255-264, June.
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    Keywords

    Interacting Particle Systems; duality;

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