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Asymptotic Behaviour of the Critical Value for the Contact Process with Rapid Stirring

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Abstract

We study the behaviour of the contact process with rapid stirring on the lattice \(\mathbb Z ^d\) in dimensions \(d\ge 3.\) This process was studied earlier by Konno and Katori, who proved results for the speed of convergence of the critical value as the rate of stirring approaches infinity. In this article we improve the results of Konno and Katori and establish the sharp asymptotics of the critical value in dimensions \(d\ge 3.\)

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References

  1. Bramson, M., Durrett, R., Swindle, G.: Statistical mechanics of crab grass. Ann. Probab. 17, 444–481 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. DeMassi, A., Ferrari, P.A., Lebowitz, J.L.: Reaction-diffusion equations for interacting particle systems. J. Stat. Phys. 44(3), 589–644 (1986)

    Article  Google Scholar 

  3. Durret, R., Neuhauser, C.: Particle systems and reaction-diffusion equations. Ann. Probab. 2(1), 289–333 (1994)

    Article  Google Scholar 

  4. Durrett, R., Perkins, E.A.: Rescaled contact processes converge to super-Brownian motion for d\(\ge \)2. Probab. Theory Relat. Fields 114, 309–399 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Katori, M.: Rigorous results for the diffusive contact processes in \(d\ge 3\). J. Phys A Math. Gen. 27, 7327–7341 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. Konno, N.: Asymptotic behavior of basic contact process with rapid stirring. J. Theor. Probab. 8(4), 833–876 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Liggett, M.L.: Interacting Particle Systems. Spinger, New York (1985)

    Book  MATH  Google Scholar 

  8. Liggett, M.L.: Interacting Particle Systems: Contact, Voter and Exclusion Processes. Spinger, New York (1991)

    Google Scholar 

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Acknowledgments

Both authors thank an anonymous referee for the careful reading of the manuscript and for a number of useful comments and suggestions that improved the exposition. Supported by the ISF grant 497/10.

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Authors and Affiliations

  1. Faculty of Industrial Engineering and Management Technion, Israel Institute of Technology, 32000 , Haifa, Israel

    Roman Berezin & Leonid Mytnik

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  1. Roman Berezin
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  2. Leonid Mytnik
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Correspondence to Roman Berezin.

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Berezin, R., Mytnik, L. Asymptotic Behaviour of the Critical Value for the Contact Process with Rapid Stirring. J Theor Probab 27, 1045–1057 (2014). https://doi.org/10.1007/s10959-012-0470-z

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  • DOI: https://doi.org/10.1007/s10959-012-0470-z

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