Dyson diffusion on a curved contour
A. Zabrodin
TL;DR
This paper introduces a Dyson diffusion process on a curved contour, deriving its Fokker-Planck equation and showing the stationary distribution corresponds to a Boltzmann weight for a logarithmic gas on that contour.
Contribution
It extends Dyson diffusion to curved contours and derives the associated Fokker-Planck equation with a novel stationary solution.
Findings
Stationary distribution is Boltzmann weight for logarithmic gas
Fokker-Planck equation derived for the process
Diffusion defined on a curved smooth closed contour
Abstract
We define the Dyson diffusion process on a curved smooth closed contour in the plane and derive the Fokker-Planck equation for probability density. Its stationary solution is shown to be the Boltzmann weight for the logarithmic gas confined on the contour.
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Taxonomy
TopicsDiffusion and Search Dynamics · Stochastic processes and statistical mechanics · Mathematical Biology Tumor Growth