High temperature limits for $(1+1)$-dimensional directed polymer with heavy-tailed disorder
High temperature limits for $(1+1)$-dimensional directed polymer with heavy-tailed disorder
复制标题
具有重尾无序的 $(1 1)$ 维定向聚合物的高温极限
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Nikos Zygouras
中科院分区：
文献类型：
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作者：
P. Dey;Nikos Zygouras
Alberts-Khanin-Quastel[Ann]提出了中等无序区的定向聚合物模型。可能吧。42(2014)1212-1256]。证明了在逆温度βn−γβn−γ且γ=1/4γ=1/4的条件下，配分函数以适当的中心按分布收敛，并且极限由随机热方程的解给出.这一结果是在无序变量具有指数矩的假设下得到的，但其普适性也是在六矩假设下得到的。我们证明了这一猜想是有效的，并进一步推广了这一猜想，在不超过6个力矩的情况下展示了几类不同的普遍极限行为。我们还解释了在不同的矩假设和γγ取值下对数分配函数的标度指数的行为。
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−γβn−γ with γ=1/4γ=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 γγ.
影响因子：
2.6
作者：
F. Caravenna;Rongfeng Sun;Nikos Zygouras
通讯作者：
F. Caravenna;Rongfeng Sun;Nikos Zygouras
影响因子：
2.5
作者：
Corwin, Ivan;O'Connell, Neil;Zygouras, Nikolaos
通讯作者：
Zygouras, Nikolaos