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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

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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
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:
DateEvent
14 November 2016Published
1 September 2015Accepted
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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