Hitting Probability of a Distant Point for the Voter Model Started with a Single One

@inproceedings{Merle2006HittingPO,
  title={Hitting Probability of a Distant Point for the Voter Model Started with a Single One},
  author={Mathieu Merle},
  year={2006}
}
  • Mathieu Merle
  • Published 2006
The goal of this work is to find the asymptotics of the hitting probability of a distant point for the voter model on the integer lattice started from a single 1 at the origin. In dimensions d = 2 or 3, we obtain the precise asymptotic behaviour of this probability. We use the scaling limit of the voter model started from a single 1 at the origin in terms of super-Brownian motion under its excursion measure. This invariance principle was stated by Bramson, Cox and Le Gall, as a consequence of a… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 21 references

Spatial Branching Processes, The Brownian Snake and Partial Differential Equations, Birkhäuser

  • Le Gall J.-F
  • 1999
Highly Influential
15 Excerpts

Dawson-Watanabe Superprocesses and Measure-valued Diffusions, Lectures on Probability Theory and Statistics

  • E. A. Perkins
  • Ecole d’été de Probabilités de Saint-Flour…
  • 1999
Highly Influential
4 Excerpts

The Hausdorff Measure of the Support of Two-dimensional Super-Brownian Motion

  • Le Gall J.-F, Perkins E.A
  • The Annals of Probability,
  • 1995
Highly Influential
5 Excerpts

Intersections of Random Walks, Probability and Its Applications, Birkhäuser

  • G. F. Lawler
  • 1991
Highly Influential
4 Excerpts

Probability in Banach Spaces, Springer-Verlag, New-York

  • M. Ledoux, M. Talagrand
  • 1991
Highly Influential
3 Excerpts

Asymptotics for Interacting Particle Systems on Z

  • M. Bramson, D. Griffeath
  • Zeitschrift fur Wahrscheinlichkeitstheorie und…
  • 1980
Highly Influential
8 Excerpts

Stochastic evolution equations and related measure-valued processes

  • D. A. Dawson
  • Journal of Multivariate Analysis,
  • 1975
Highly Influential
5 Excerpts

Some Properties of the Range of Super-Brownian Motion

  • Delmas J.-F
  • Probability Theory and Related Fields,
  • 1999

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