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.
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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
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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
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DOI: https://doi.org/10.1007/s004400200213