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Polymers on disordered trees, spin glasses, and traveling waves.(English)Zbl 1036.82522

Self-avoiding walks (directed polymers) in a random potential on a Cayley tree are studied. The generating function for the partition function is shown to satisfy the Kolmogorov-Petrovskii-Piskunov equation. By results of Bramson, it is shown that there is a transition which is similar to the random energy model.

MSC:

82D60 Statistical mechanics of polymers
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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