ON POLYMER CONFORMATIONS IN ELONGATIONAL FLOWS

We consider various models of polymer conformations using paths of Gau ssian processes such as Brownian motion. In each case, the calculation of the law of the moment of inertia of a random polymer structure (wh ich is equivalent to the calculation of the partition function) is red uced to the problem of finding the law of a certain quadratic function al of a Gaussian process. We present a new method for computing the La place transforms of these quadratic functionals which exploit their sp ecial form via the Ray-Knight Theorem and which does not involve the c lassical method of eigenvalue expansions. We apply the method to sever al simple examples, then show how the same techniques can be applied t o more complicated cases with the aid of a little excursion theory.