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High temperature limits for $(1+1)$-dimensional directed polymer with heavy-tailed disorder
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Dey, Partha S. and Zygouras, Nikos (2016) High temperature limits for $(1+1)$-dimensional directed polymer with heavy-tailed disorder. The Annals of Probability, 44 (6). pp. 4006-4048. doi:10.1214/15-AOP1067
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Official URL: http://dx.doi.org/10.1214/15-AOP1067
Abstract
The directed polymer model at intermediate disorder regime was introduced by Alberts–Khanin–Quastel [Ann. Probab. 42 (2014) 1212–1256]. It was proved that at inverse temperature βn−γ with γ=1/4 the partition function, centered appropriately, converges in distribution and the limit is given in terms of the solution of the stochastic heat equation. This result was obtained under the assumption that the disorder variables posses exponential moments, but its universality was also conjectured under the assumption of six moments. We show that this conjecture is valid and we further extend it by exhibiting classes of different universal limiting behaviors in the case of less than six moments. We also explain the behavior of the scaling exponent for the log-partition function under different moment assumptions and values of γ.
| Item Type: | Journal Article | ||||||
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| Divisions: | Faculty of Science > Statistics | ||||||
| Journal or Publication Title: | The Annals of Probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 0091-1798 | ||||||
| Official Date: | 14 November 2016 | ||||||
| Dates: |
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| Volume: | 44 | ||||||
| Number: | 6 | ||||||
| Page Range: | pp. 4006-4048 | ||||||
| DOI: | 10.1214/15-AOP1067 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
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