The near-critical scaling window for directed polymers on disordered trees
- Creators
- Alberts, Tom
- Ortgiese, Marcel
Abstract
We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on the asymptotics of the partition function in the near-critical regime, where the inverse temperature is a small perturbation away from the critical one with the perturbation converging to zero as the system size grows large. Depending on the speed of convergence we observe very different asymptotic behavior. If the perturbation is small then we are inside the critical window and observe the same decay of the partition function as at the critical temperature. If the perturbation is slightly larger the near critical scaling leads to a new range of asymptotic behaviors, which at the extremes match up with the already known rates for the sub- and super-critical regimes. We use our results to identify the size of the fluctuations of the typical energies under the critical Gibbs measure.
Additional Information
© 2013 Institute of Mathematical Statistics. This work is licensed under a Creative Commons Attribution 3.0 License. Submitted to EJP on May 18, 2012, final version accepted on January 25, 2013. Publication Date: January 30, 2013. Supersedes arXiv:1205.0737v1. We thank the referee for a careful reading of the paper and some helpful comments and suggestions on the presentation. We thank the organizers of the 2010 PIMS Summer School in Probability, where this project originated, and the Fields Institute for hosting us while most of this work was completed. We also thank the organizers of the 2011 Fields Thematic Program on Dynamics and Transport in Disordered Systems for the invitation to the program.Attached Files
Published - 2036-12569-1-PB.pdf
Submitted - 1205.0737.pdf
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Additional details
- Eprint ID
- 37427
- Resolver ID
- CaltechAUTHORS:20130308-155500533
- Created
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2013-03-11Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field