Tightness is proved for reversible gradient dynamics of critical strip-wetting models, and a new continuous wetting measure with a local-time tilt converges to reflecting Brownian motion as the strip shrinks, leaving a Bessel SPDE as the conjectured limit.
Bessel SPDEs with general Dirichlet boundary conditions
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abstract
We generalise the integration by parts formulae obtained in arXiv:1811.00518v5 [math.PR] to Bessel bridges on $[0,1]$ with arbitrary boundary values, as well as Bessel processes with arbitrary initial conditions. This allows us to write, formally, the corresponding dynamics using renormalised local times, thus extending the Bessel SPDEs of arXiv:1811.00518v5 [math.PR] to general Dirichlet boundary conditions. We also prove a dynamical result for the case of dimension $2$, by providing a weak construction of the gradient dynamics corresponding to a $2$-dimensional Bessel bridge.
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On the gradient dynamics associated with wetting models
Tightness is proved for reversible gradient dynamics of critical strip-wetting models, and a new continuous wetting measure with a local-time tilt converges to reflecting Brownian motion as the strip shrinks, leaving a Bessel SPDE as the conjectured limit.