Comets, Francis; Shiga, Tokuzo; Yoshida, Nobuo Directed polymers in a random environment: Path localization and strong disorder. (English) Zbl 1042.60069 Bernoulli 9, No. 4, 705-723 (2003). Directed polymers in a random environment are investigated. Using martingale decomposition and martingale analysis there are proven: equivalence between the decay rate of the partition function and some natural localization properties of the path; some quantitative estimates of the decay of the partition function in one or two dimensions, or at sufficiently low temperature; the existence of quenched free energy. In particular, the results of Carmona and Hu are generalized to general environments. Reviewer: Utkir Rozikov (Tashkent) Cited in 1 ReviewCited in 80 Documents MSC: 60K37 Processes in random environments 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics Keywords:directed polymers; martingales; random environment × Cite Format Result Cite Review PDF Full Text: DOI Euclid