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The Initial Drift of a 2D Droplet at Zero Temperature

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

Mathematics Subject Classification (2000)

  • 60K35
  • 82C22