The 3D attractive one-point interaction diffusion visits the origin with positive probability; conditioning on never visiting yields standard 3D Wiener measure.
Chen:The critical 2D delta-Bose gas as mixed-order asymptotics of planar Brownian motion, arXiv:2105.05154 (2021)
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Constructs a time-inhomogeneous Markov process on dyadic times for the 3D attractive point interaction via limiting sub-probability kernels from iterated Doob transforms and dyadic refinements, extended with a cemetery state.
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Pathwise structure of the three-dimensional attractive one-point interaction diffusion
The 3D attractive one-point interaction diffusion visits the origin with positive probability; conditioning on never visiting yields standard 3D Wiener measure.
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A dyadic construction of a three-dimensional attractive point interaction Markov family
Constructs a time-inhomogeneous Markov process on dyadic times for the 3D attractive point interaction via limiting sub-probability kernels from iterated Doob transforms and dyadic refinements, extended with a cemetery state.