SEMIFLEXIBLE POLYMER IN THE HALF-PLANE AND STATISTICS OF THE INTEGRAL OF A BROWNIAN CURVE

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.