On the partition function of a directed polymer in a Gaussian random environment

 The purpose of this work is the study of the partition function of a -dimensional lattice directed polymer in a Gaussian random environment being the inverse of temperature). In the low-dimensional cases , we prove that for all , the renormalized partition function converges to 0 and the correlation of two independent configurations does not converge to 0. In the high dimensional case (), a lower tail of has been obtained for small . Furthermore, we express some thermodynamic quantities in terms of the path measure alone. Received: 8 June 2001 / Revised version: 8 February 2002 / Published online: 22 August 2002 Mathematics Subject Classification (2000): 60K37, 82D30 Key words or phrases: Directed polymer in random environment – Gaussian environment – partition function