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November 2016 High temperature limits for $(1+1)$-dimensional directed polymer with heavy-tailed disorder
Partha S. Dey, Nikos Zygouras
Ann. Probab. 44(6): 4006-4048 (November 2016). DOI: 10.1214/15-AOP1067


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 $\beta n^{-\gamma}$ with $\gamma=1/4$ 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 $\gamma$.


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Partha S. Dey. Nikos Zygouras. "High temperature limits for $(1+1)$-dimensional directed polymer with heavy-tailed disorder." Ann. Probab. 44 (6) 4006 - 4048, November 2016.


Received: 1 April 2015; Revised: 1 September 2015; Published: November 2016
First available in Project Euclid: 14 November 2016

zbMATH: 1359.60117
MathSciNet: MR3572330
Digital Object Identifier: 10.1214/15-AOP1067

Primary: 60F05 , 82D60
Secondary: 60G57 , 60G70

Keywords: Directed polymer , heavy tail , phase transition , scaling limits

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 6 • November 2016
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