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Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems: a theoretical and experimental study

Isabelle Gaudron (2010)

ESAIM: Probability and Statistics

We study in this paper the convergence rate of the Swendsen-Wang dynamics towards its equilibrium law, when the energy belongs to a large family of energies used in image segmentation problems. We compute the exponential equivalents of the transitions which control the process at low temperature, as well as the critical constant which gives its convergence rate. We give some theoretical tools to compare this dynamics with Metropolis, and develop an experimental study in order to calibrate...

Regularity of the effective diffusivity of random diffusion with respect to anisotropy coefficient

M. Cudna, T. Komorowski (2008)

Studia Mathematica

We show that the effective diffusivity of a random diffusion with a drift is a continuous function of the drift coefficient. In fact, in the case of a homogeneous and isotropic random environment the function is C ∞ smooth outside the origin. We provide a one-dimensional example which shows that the diffusivity coefficient need not be differentiable at 0.

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