Free energy fluctuations for a mixture of directed polymers

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• 作者：ZhongGen Su
• 关键词：free energy ; KPZ universality class ; log ; Gamma directed polymer ; O’Connell ; Yor semi ; discrete directed polymer ; Tracy ; Widom law
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：60
• 期：3
• 页码：511-528
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

We study the free energy fluctuations for a mixture of directed polymers, which was first introduced by Borodin et al. (2015) to investigate the limiting distribution of a stationary Kardar-Parisi-Zhang (KPZ) equation. The main results consist of both the law of large numbers and the asymptotic fluctuation for the free energy as the model size tends to infinity. In particular, we find the explicit values (which may depend on model parameters) of normalizing constants in the fluctuation. This shows that such a mixture model is in the KPZ university class.