Tracy–Widom fluctuations for perturbations of the log-gamma polymer in intermediate disorder
Tracy–Widom fluctuations for perturbations of the log-gamma polymer in intermediate disorder
复制标题
中间无序中对数伽马聚合物扰动的 Tracy-Widom 涨落
DOI：
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发表时间：
2016
期刊：
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通讯作者：
J. Quastel
中科院分区：
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作者：
Arjun Krishnan;J. Quastel
据推测，在所有有限温度和中间无序状态下，离散定向聚合物在 1+1 维度上的自由能涨落属于 Tracy-Widom 普适类。 Borodin 等人证明 Sepp\"al\"ainen 的 log-gamma 聚合物在有限的温度范围内具有 GUE Tracy-Widom 波动。等人。 （2013）。我们取消了这个限制，并将这个结果扩展到中间无序状态。该结果还确定了中间无序状态下log-gamma聚合物的波动规模，从而验证了Alberts等人的猜想。等人。 （2010）。使用微扰论证，我们证明任何与 log-gamma 聚合物匹配一定数量矩的聚合物也具有中间无序的 Tracy-Widom 波动。
The free-energy fluctuations of the discrete directed polymer in 1+1 dimensions is conjecturally in the Tracy-Widom universality class at all finite temperatures and in the intermediate disorder regime. Sepp\"al\"ainen's log-gamma polymer was proven to have GUE Tracy-Widom fluctuations in a restricted temperature range by Borodin et. al. (2013). We remove this restriction, and extend this result into the intermediate disorder regime. This result also identifies the scale of fluctuations of the log-gamma polymer in the intermediate disorder regime, and thus verifies a conjecture of Alberts et. al. (2010). Using a perturbation argument, we show that any polymer that matches a certain number of moments with the log-gamma polymer also has Tracy-Widom fluctuations in intermediate disorder.