An application of the voter model–super-brownian motion invariance principle

J. Theodore Cox; Edwin A. Perkins

Annales de l'I.H.P. Probabilités et statistiques (2004)

  • Volume: 40, Issue: 1, page 25-32
  • ISSN: 0246-0203

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Cox, J. Theodore, and Perkins, Edwin A.. "An application of the voter model–super-brownian motion invariance principle." Annales de l'I.H.P. Probabilités et statistiques 40.1 (2004): 25-32. <http://eudml.org/doc/77796>.

@article{Cox2004,
author = {Cox, J. Theodore, Perkins, Edwin A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Voter model; Super-Brownian motion},
language = {eng},
number = {1},
pages = {25-32},
publisher = {Elsevier},
title = {An application of the voter model–super-brownian motion invariance principle},
url = {http://eudml.org/doc/77796},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Cox, J. Theodore
AU - Perkins, Edwin A.
TI - An application of the voter model–super-brownian motion invariance principle
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2004
PB - Elsevier
VL - 40
IS - 1
SP - 25
EP - 32
LA - eng
KW - Voter model; Super-Brownian motion
UR - http://eudml.org/doc/77796
ER -

References

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  1. [1] R. Arratia, Limiting point processes for rescaling of coalescing and annihilating random walks on Zd, Ann. Probab.9 (1981) 909-936. Zbl0496.60098MR632966
  2. [2] M. Bramson, J.T. Cox, J.-F. Le Gall, Super-Brownian limits of voter model clusters, Ann. Probab.29 (2001) 1001-1032. Zbl1029.60078MR1872733
  3. [3] M. Bramson, D. Griffeath, Asymptotics for interacting particle systems on Zd, Z. Wahrsch. Verw. Geb.53 (1980) 183-196. Zbl0417.60097MR580912
  4. [4] J.T. Cox, R. Durrett, E.A. Perkins, Rescaled voter models converge to super-Brownian motion, Ann. Probab.28 (2000) 185-234. Zbl1044.60092MR1756003
  5. [5] S.N. Ethier, T.G. Kurtz, Markov Process: Characterization and Convergence, Wiley, New York, 1986. Zbl0592.60049MR838085
  6. [6] T.M. Liggett, Interacting Particle Systems, Springer, New York, 1985. Zbl1103.82016MR776231
  7. [7] E.A. Perkins, Dawson–Watanabe superprocesses and measure-valued diffusions, in: Lectures on Probability Theory and Statistics; École d'Eté des Probabilités de St. Flour XXIX, 1999, Lecture Notes in Math., vol. 1781, Springer, 2002. Zbl1020.60075
  8. [8] S. Sawyer, A limit theorem for patch sizes in a selectively-neutral migration model, J. Appl. Probab.16 (1979) 482-495. Zbl0433.92017MR540786

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