Directed polymers on hierarchical lattices with site disorder

Hubert Lacoin and Gregorio Moreno

Stochastic Processes and their Applications, 2010, vol. 120, issue 4, 467-493

Abstract: We study a polymer model on hierarchical lattices very close to the one introduced and studied in Derrida and Griffith (1989)Â [19] and Cook and Derrida (1989)Â [16]. For this model, we prove the existence of free energy and derive the necessary and sufficient condition for which very strong disorder holds for all [beta], and give some accurate results on the behavior of the free energy at high temperature. We obtain these results by using a combination of fractional moment method and change of measure over the environment to obtain an upper bound, and a second moment method to get a lower bound. We also get lower bounds on the fluctuation exponent of logZn, and study the infinite polymer measure in the weak disorder phase.

Keywords: Hierarchical; models; Free; energy; Dynamical; system; Directed; polymers (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (5)

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