Exact analyses on integrable stochastic processes related to the KPZ equation

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800215
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Chiba University
• Principal Investigator: Imamura Takashi 千葉大学, 理学(系)研究科(研究院), 准教授 (70538280)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 確率過程 / 可積分系 / KPZ方程式 / ランダム行列

Outline of Final Research Achievements

We have studied some integrable structures in the stochastic processes belonging to the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class: for the KPZ equation, we analyzed the KPZ equation using the replica approach and found out that the long time limit of the spatial two-point height correlation function obtained by V. Dotsenko is equivalent to the stochastic process called the Airy_2 process . We also considered determinantal structures for the O'Connell-Yor polymer model and clarified a relation to the GUE random matrices.

Free Research Field

非平衡統計物理学