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• W2990898231 abstract "We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $alpha in (0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, that is, when the inverse temperature temperature $beta =beta_{n}$ vanishes as the size of the system $n$ goes to infinity. When $alpha in (1/2,2)$, we show that all possible transversal fluctuations $sqrt{n}leq h_{n}leq n$ can be achieved by tuning properly $beta_{n}$, allowing to interpolate between all superdiffusive scales. Moreover, we determine the scaling limit of the model, answering a conjecture by Dey and Zygouras [Ann. Probab. 44 (2016) 4006–4048]—we actually identify five different regimes. On the other hand, when $alpha <1/2$, we show that there are only two regimes: the transversal fluctuations are either $sqrt{n}$ or $n$. As a key ingredient, we use the Entropy-controlled Last-Passage Percolation (E-LPP), introduced in a companion paper [Ann. Appl. Probab. 29 (2019) 1878–1903]." @default.
• W2990898231 created "2019-12-05" @default.
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• W2990898231 date "2019-11-01" @default.
• W2990898231 modified "2023-10-02" @default.
• W2990898231 title "Directed polymers in heavy-tail random environment" @default.
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• W2990898231 doi "https://doi.org/10.1214/19-aop1353" @default.
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