| Abstract: |
| Diffusion in Coulomb environment and a phase transition.
Hirofumi Osada (Kyushu University)
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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