95-143 Servet Martinez, Dimitri Petritis

Thermodynamics of a Brownian bridge polymer model in a random environment (109K, uuencoded postscript) Mar 9, 95

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Abstract. We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditionned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connfiguration; the random walk acts as the random environment. This model provides a continuum version of a model with some relevance to protein conformation. The thermodynamic limit of the specific free energy is shown to exist and to be self-averaging, i.e. it is equal to a trivial --- explicitely computed --- random variable. An estimate of the asymptotic behaviour of the ground state energy is also obtained.

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