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The Initial Drift of a 2D Droplet at Zero Temperature

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Abstract

We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are suitable approximations of smooth domains. A specific spatial average of the derivative at time 0 of the volume variation of a droplet close to a boundary point is equal to its curvature multiplied by a direction dependent coefficient. We compute the explicit value of this coefficient.

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Correspondence to Sana Louhichi.

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Cerf, R., Louhichi, S. The Initial Drift of a 2D Droplet at Zero Temperature. Probab. Theory Relat. Fields 137, 379–428 (2007). https://doi.org/10.1007/s00440-006-0007-4

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Keywords

  • 2D Ising model
  • Glauber dynamics
  • Zero temperature
  • Markov process
  • Mean curvature
  • Velocity

Mathematics Subject Classification (2000)

  • 60K35
  • 82C22