Journal of Statistical Physics

, Volume 89, Issue 3, pp 581–603

Directed polymers in a random environment: Some results on fluctuations

  • M. S. T. Piza

DOI: 10.1007/BF02765537

Cite this article as:
Piza, M.S.T. J Stat Phys (1997) 89: 581. doi:10.1007/BF02765537


We consider a polymer model on ℤ+d where to each edgee is associated a random variable v(e). A polymer configuration is represented by a directed pathr and has a weight exp[-βerν(e)], withβ=1/T the inverse temperature. We extend some rigorous results that have been obtained for the ground state of this model to finite temperatures. In particular we obtain some upper and lower bounds on sample-to-sample free energy fluctuations, and also rigorous scaling inequalities between the exponents describing free energy fluctuations and transversal displacements of polymer configurations

Key Words

Directed polymers random environment scaling relations free energy variance 

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • M. S. T. Piza
    • 1
  1. 1.Statistical LaboratoryUniversity of CambridgeCambridgeUK