Exact analyses on integrable stochastic processes related to the KPZ equation

• 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
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 確率過程 / 可積分系 / KPZ方程式 / ランダム行列 / KPZクラス / レプリカ法

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.

Research Products

• [Journal Article] Determinantal structures in the O’Connell-Yor directed random polymer model (2016)
  • Author(s): Takashi Imamura, Tomohiro Sasamoto
  • Journal Title: J. Stat. Phys. Volume: 印刷中 Issue: 4 Pages: 675-713
  • DOI: 10.1007/s10955-016-1492-1
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the equal time two-point distribution of the one-dimensional KPZ equation by replica (2013)
  • Author(s): Takashi Imamura, Tomohiro Sasamoto, Herbert Spohn
  • Journal Title: J. Phys. A: Math. Theor. Volume: 46 Issue: 35 Pages: 355002-355002
  • DOI: 10.1088/1751-8113/46/35/355002
  • Peer Reviewed
• [Presentation] O'Connell-Yor ランダムポリマーモデルにおける ゆらぎの厳密な解析 (2016)
  • Author(s): 今村 卓史
  • Organizer: 日本物理学会第71回年次大会
  • Place of Presentation: 東北学院大学泉キャ ンパス(宮城県仙台市泉区)
  • Year and Date: 2016-03-21
• [Presentation] Determinantal structures in the O'Connell-Yor polymer model (2016)
  • Author(s): Takashi Imamura
  • Organizer: New approaches to non-equilibrium and random systems: KPZ integrability, universality, applications and experiments
  • Place of Presentation: Kavli Institute for Theoretical Physcs, University of California, Santa Barbara, USA
  • Year and Date: 2016-03-09
  • Int'l Joint Research / Invited
• [Presentation] Determinantal structures in a random polymer model (2016)
  • Author(s): Takashi Imamura
  • Organizer: RIKKYO MathPhys 2016
  • Place of Presentation: 立教大学(東京都豊島区)
  • Year and Date: 2016-01-10
  • Int'l Joint Research / Invited
• [Presentation] O'Connell-Yor ランダムポリマーモデルにおける 行列式構造 (2015)
  • Author(s): 今村 卓史
  • Organizer: 日本数学会2015年度秋季総合分科会
  • Place of Presentation: 京都産業大学(京都府京都市北区)
  • Year and Date: 2015-09-13
• [Presentation] Determinantal structures in the O'Connell-Yor polymer (2015)
  • Author(s): Takashi Imamura
  • Organizer: The 8th International Conference on Industrial and Applied Mathematics
  • Place of Presentation: China National Convention Center, Beijing, China
  • Year and Date: 2015-08-11
  • Int'l Joint Research / Invited
• [Presentation] Determinantal structures in the O'Connell-Yor directed random polymer model (2015)
  • Author(s): Takashi Imamura
  • Organizer: 38th Conference on Stochastic Processes and their Applications
  • Place of Presentation: University of Oxford, Oxford,UK
  • Year and Date: 2015-07-16
  • Int'l Joint Research
• [Presentation] From q-TASEP to SHE (2015)
  • Author(s): 今村卓史
  • Organizer: Random matrices, determinantal processes and integrable probability
  • Place of Presentation: 大分国際交流会館
  • Year and Date: 2015-03-07
  • Invited
• [Presentation] The O'Connell-Yor polymer and a deformed GUE weight (2015)
  • Author(s): 今村卓史
  • Organizer: ランダム作用素のスペクトルと関連する話題
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-01-09
  • Invited
• [Presentation] Exact height distribution for the stationary one-dimensional Kardar-Parisi-Zhang equation (2013)
  • Author(s): Takashi Imamura
  • Organizer: STATPHYS25
  • Place of Presentation: Seoul National University, Seoul, Korea
• [Presentation] Replica analysis of the one-dimensional Kardar-Parisi-Zhang equation (2013)
  • Author(s): Takashi Imamura
  • Organizer: Mathematical Statistical Physics
  • Place of Presentation: 京都大学基礎物理学研究所
• [Presentation] Replica approach to the 1d KPZ equation (2013)
  • Author(s): 今村 卓史
  • Organizer: 京大基研セミナー
  • Place of Presentation: 京都大学基礎物理学研究所
  • Invited
• [Remarks] IOP select
  • URL: http://m.iopscience.iop.org/1751-8121/46/35/355002
• [Remarks] Highlights of 2013
  • URL: http://iopscience.iop.org/1751-8121/page/Highlights-of-2013