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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 

Pages (fromto)  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
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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