  We consider the Brownian directed polymer in Poissonian environment in
dimension 1+1, under the so-called intermediate disorder regime, which is a
crossover regime between the strong and weak disorder regions. We show that,
under a diffusive scaling involving different parameters of the system, the
renormalized point-to-point partition function of the polymer converges in law
to the solution of the stochastic heat equation with Gaussian multiplicative
noise. The Poissonian environment provides a natural setting and strong tools,
such as the Wiener-Ito chaos expansion, which, applied to the partition
function, is the basic ingredient of the proof.
