Projects per year

### Abstract

We consider a model of directed polymers on a regular tree with a disorder given by independent, identically distributed weights attached to the vertices. For suitable weight distributions this model undergoes a phase transition with respect to its localization behavior. We show that, for high temperatures, the free energy is supported by a random tree of positive exponential growth rate, which is strictly smaller than that of the full tree. The growth rate of the minimal supporting subtree decreases to zero as the temperature decreases to the critical value. At the critical value and all lower temperatures, a single polymer suffices to support the free energy. Our proofs rely on elegant martingale methods adapted from the theory of branching random walks.

Original language | English |
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Pages (from-to) | 125203 |

Number of pages | 1 |

Journal | Journal of Mathematical Physics |

Volume | 49 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2008 |

### Keywords

- phase transformations
- free energy
- polymer structure
- polymers

## Fingerprint Dive into the research topics of 'Minimal supporting subtrees for the free energy of polymers on disordered trees'. Together they form a unique fingerprint.

## Projects

- 2 Finished

### INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA

Morters, P.

Engineering and Physical Sciences Research Council

1/09/05 → 31/08/10

Project: Research council

### STOCHASTIC PROCESSES IN RANDOM MEDIA: AN APPROACH USING INT ERSECTION LOCAL TIMES

Morters, P.

Engineering and Physical Sciences Research Council

1/04/05 → 30/04/08

Project: Research council

## Cite this

Morters, P., & Ortgiese, M. (2008). Minimal supporting subtrees for the free energy of polymers on disordered trees.

*Journal of Mathematical Physics*,*49*(12), 125203. https://doi.org/10.1063/1.2962981