Directed polymers on trees: a martingale approach
- 21 April 1993
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 26 (8) , 1823-1834
- https://doi.org/10.1088/0305-4470/26/8/011
Abstract
The authors use martingale methods and simple convexity arguments to compute rigorously the limiting free energy in the problem of directed polymers on a tree. The limit is a degenerate random variable and convergence holds almost surely. The only assumption on the common distribution of the random potentials attached to the bonds of the tree is that its Laplace transform exists everywhere in (0, infinity ).Keywords
This publication has 12 references indexed in Scilit:
- Finite-size effects in random energy models and in the problem of polymers in a random mediumJournal of Statistical Physics, 1991
- Lyapunov exponents of large, sparse random matrices and the problem of directed polymers with complex random weightsJournal of Statistical Physics, 1990
- Directed polymers in a random mediumPhysica A: Statistical Mechanics and its Applications, 1990
- A note on the diffusion of directed polymers in a random environmentCommunications in Mathematical Physics, 1989
- Polymers on disordered hierarchical lattices: A nonlinear combination of random variablesJournal of Statistical Physics, 1989
- Diffusion of directed polymers in a random environmentJournal of Statistical Physics, 1988
- Polymers on disordered trees, spin glasses, and traveling wavesJournal of Statistical Physics, 1988
- Pinning and Roughening of Domain Walls in Ising Systems Due to Random ImpuritiesPhysical Review Letters, 1985
- Random-Energy Model: Limit of a Family of Disordered ModelsPhysical Review Letters, 1980
- The First Birth Problem for an Age-dependent Branching ProcessThe Annals of Probability, 1975