Abstract.
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.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Author information
Authors and Affiliations
Additional information
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
Rights and permissions
About this article
Cite this article
Carmona, P., Hu, Y. On the partition function of a directed polymer in a Gaussian random environment. Probab Theory Relat Fields 124, 431–457 (2002). https://doi.org/10.1007/s004400200213
Issue Date:
DOI: https://doi.org/10.1007/s004400200213