Semiflexible polymer in the half plane and statistics of the integral of a Brownian curve

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Abstract
A continuum model of a polymer with non-zero bending energy, fluctuating without overhangs in the half plane, is considered. The exact partition function is obtained from the Marshall-Watson solution of the Klein-Kramers equation for Brownian motion in the half space. The partition function contains information on probabilities associated with the integral of a Brownian curve and reproduces Sinai's t-5/4 result for the asymptotic first passage time density. The t-5/2 dependence of a different passage probability implies a first-order polymer adsorption transition for short-range pinning potentials.