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The noisy voter model

Author

Listed:
  • Granovsky, Boris L.
  • Madras, Neal

Abstract

The noisy voter model is a spin system on a graph which may be obtained from the basic voter model by adding spontaneous flipping from 0 to 1 and from 1 to 0 at each site. Using duality, we obtain exact formulas for some important time-dependent and equilibrium functionals of this process. By letting the spontaneous flip rates tend to zero, we get the basic voter model, and we calculate the exact critical exponents associated with this "phase transition". Finally, we use the noisy voter model to present an alternate view of a result due to Cox and Griffeath on clustering in the two-dimensional basic voter model.

Suggested Citation

  • Granovsky, Boris L. & Madras, Neal, 1995. "The noisy voter model," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 23-43, January.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:1:p:23-43
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    Citations

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    Cited by:

    1. Ted Theodosopoulos, 2004. "Uncertainty relations in models of market microstructure," Papers math/0409076, arXiv.org, revised Feb 2005.
    2. Kyrylo Shmatov & Mikhail Smirnov, 2005. "On Some Processes and Distributions in a Collective Model of Investors' Behavior," Papers nlin/0506015, arXiv.org.
    3. Khalil, Nagi, 2021. "Approach to consensus in models of continuous-opinion dynamics: A study inspired by the physics of granular gases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    4. Granovsky, Boris L. & Zeifman, Alexander I., 1997. "The decay function of nonhomogeneous birth-death processes, with application to mean-field models," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 105-120, December.
    5. Theodosopoulos, Ted & Yuen, Ming, 2007. "Properties of the wealth process in a market microstructure model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 443-452.
    6. Theodosopoulos, Ted, 2005. "Uncertainty relations in models of market microstructure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 209-216.
    7. Adri'an Carro & Ra'ul Toral & Maxi San Miguel, 2016. "The noisy voter model on complex networks," Papers 1602.06935, arXiv.org, revised Apr 2016.
    8. Volker Hösel & Johannes Müller & Aurelien Tellier, 2019. "Universality of neutral models: decision process in politics," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-8, December.
    9. Jung, Paul, 2005. "The noisy voter-exclusion process," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1979-2005, December.
    10. Peralta, Antonio F. & Khalil, Nagi & Toral, Raúl, 2020. "Ordering dynamics in the voter model with aging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).
    11. Lee, Woosub & Yang, Seong-Gyu & Kim, Beom Jun, 2022. "The effect of media on opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    12. Alili, Smail & Ignatiouk-Robert, Irina, 2001. "On the surviving probability of an annihilating branching process and application to a nonlinear voter model," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 301-316, June.
    13. Chen, Yu-Ting & Cox, J. Theodore, 2018. "Weak atomic convergence of finite voter models toward Fleming–Viot processes," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2463-2488.
    14. Khalil, Nagi & Toral, Raúl, 2019. "The noisy voter model under the influence of contrarians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 81-92.
    15. Kononovicius, Aleksejus, 2021. "Supportive interactions in the noisy voter model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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