Diffusion in Coulomb environment and a phase transition.

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Date(s) - 24/02/2017
11 h 00 min - 12 h 00 min

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I talk homogenization of diffusion in two-dimensional Euclidian space in a periodic Coulomb environment.
That is, we consider a periodic point process in the plane and the diffusion has the repulsive interaction with the two-dimensional Coulomb potential with inverse temperature \beta to each particle in the periodic point process.
We first prove that the diffusion is diffusive with non-degenerated effective diffusion constant \gamma.
We then remove one particle from the environment and consider the diffusive scaling limit of the diffusion. Then its new effective constant depending on the inverse temperature \beta has a phase transition whose critical point is given explicitly in terms of the original effective diffusion constant \gamma of the periodic homogenization problem. Using this result, we present explicit bounds for the critical point of the self-diffusion matrices of the two-dimensional strict Coulomb interacting Brownian motions with respect to inverse temperature \beta.


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