The Time for a Critical Nearest Particle System to reach Equilibrium starting with a large Gap

Thomas Mountford (Departement de Mathematiques, Ecole Polytechnique Federale, Switzerland)
Li-Chau Wu (Institute of Mathematics, Academia Sinica, Taipei, Taiwan)

Abstract


We consider the time for a critical nearest particle system, starting in equilibrium subject to possessing a large gap, to achieve equilibrium.

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Pages: 436-498

Publication Date: June 13, 2005

DOI: 10.1214/EJP.v10-242

References

  • Durrett, Richard. Lecture notes on particle systems and percolation. The Wadsworth & Brooks/Cole Statistics/Probability Series. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1988. viii+335 pp. ISBN: 0-534-09462-7 MR0940469
  • Diaconis, Persi; Stroock, Daniel. Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Probab. 1 (1991), no. 1, 36--61. MR1097463
  • Ethier, S. and Kurz, T. (1989): Convergence of Markov Processes Wiley.
  • Griffeath, David; Liggett, Thomas M. Critical phenomena for Spitzer's reversible nearest particle systems. Ann. Probab. 10 (1982), no. 4, 881--895. MR0672290
  • Sinclair, Alistair; Jerrum, Mark. Approximate counting, uniform generation and rapidly mixing Markov chains. Inform. and Comput. 82 (1989), no. 1, 93--133. MR1003059
  • Kipnis, C. and Landin, C. (1998): Scaling Limits of Interacting Particle Systems. Springer, New York.
  • Liggett, Thomas M. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231
  • Mountford, Thomas. A convergence result for critical reversible nearest particle systems. Ann. Probab. 30 (2002), no. 1, 1--61. MR1894100
  • Mountford, Thomas; Sweet, Ted. Finite approximations to the critical reversible nearest particle system. Ann. Probab. 26 (1998), no. 4, 1751--1780. MR1675071
  • Mountford, T. and Wu, L.C. A Convergence Result for Critical Nearest Particle Systems in Equilibrium. In preparation.
  • Schinazi, Rinaldo. Brownian fluctuations of the edge for critical reversible nearest-particle systems. Ann. Probab. 20 (1992), no. 1, 194--205. MR1143418
  • Schonmann, Roberto H. Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region. Comm. Math. Phys. 161 (1994), no. 1, 1--49. MR1266068
  • Spitzer, Frank. Stochastic time evolution of one dimensional infinite particle systems. Bull. Amer. Math. Soc. 83 (1977), no. 5, 880--890. MR0448632
  • Wu, Li Chau. (2002): Critical Nearest Particle Systems. PhD thesis, University of California.


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