Studies of one dimensional interacting particle systems using the methods of integrable systems.

• Project/Area Number: 19740044
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Chiba University
• Principal Investigator: SASAMOTO Tomohiro Chiba University, 大学院・理学研究科, 准教授 (70332640)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,730,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥630,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 確率論 / 無限粒子系 / 可積分系 / ランダム行列 / 揺らぎ

Research Abstract

We have deepened the understanding of the fluctuation properties of one-dimensional surface growth models. For the polynuclear growth model with flat initial condition, we have identified the fluctuations and discussed its asymptotics. We have also obtained a formula for the fluctuations of the KPZ equation with wedge initial conditions. We have also found a formula of a relation between two time dependent random matrix ensembles.

Research Products

• [Journal Article] Two speed TASEP (2009)
  • Author(s): A. Borodin, P.L. Ferrari, T. Sasa moto
  • Journal Title: J. Stat. Phy s. 137 Pages: 936-977
  • Peer Reviewed
• [Journal Article] Maxi mum of Dyson Brownian motion and non-colliding system with a bounda ry (2009)
  • Author(s): A. Borodin, P.L. Ferrari, M. Praehof er, T. Sasamoto, J. Warren
  • Journal Title: Elect. Comm. Probab. 4 Pages: 486-494
  • Peer Reviewed
• [Journal Article] Superdif fusivity of the 1D lattice Kardar-Par isi-Zhang equation (2009)
  • Author(s): T. Sasamoto, H. Spohn
  • Journal Title: J. Stat. Phys. 137 Pages: 917-935
  • Peer Reviewed
• [Journal Article] Two Speed TASEP (2009)
  • Author(s): A.Borodin, P.LFerrari, T.Sasamoto
  • Journal Title: J.Stat.Phys. 137 Pages: 936-977
  • Peer Reviewed
• [Journal Article] Maximum of Dyson Brownian motion and non-colliding systems with a boundary (2009)
  • Author(s): A.Borodin, P.L.Ferrari, M.Praehofer, T.Sasamoto, J.Warren
  • Journal Title: Elect.Comm.Probab. 14 Pages: 486-494
  • Peer Reviewed
• [Journal Article] Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation (2009)
  • Author(s): T.Sasamoto, H.Spohn
  • Journal Title: J.Stat.Phys. 137 Pages: 917-935
  • Peer Reviewed
• [Journal Article] (2008)
  • Author(s): A. Borodin, P.L. Ferrari, T. Sasamoto
  • Journal Title: Comm. Pure Appl. Mth. 61 Pages: 1603-1629
  • Peer Reviewed
• [Journal Article] Large time asymptotics of gro wth models on space-like paths II:P NG and parallel TASEP (2008)
  • Author(s): A. Borodin, P.L. Ferrari, T. Sasa moto
  • Journal Title: Comm. Mat h. Phys. 283 Pages: 417-449
  • Peer Reviewed
• [Journal Article] Correl ation function of the Schur process with a fixed final partition (2008)
  • Author(s): T. Imamura, T. Sasamoto
  • Journal Title: 49 Pages: 53302-53302
  • Peer Reviewed
• [Journal Article] Exact results for the 1 D asymmetric exclusion process and KPZ fluctuations (2008)
  • Author(s): T. Sasamoto
  • Journal Title: Eur. Phys. Jour. B 64 Pages: 373-377
  • Peer Reviewed
• [Journal Article] Large time asymptotics of growth models on space-like paths II : PNG And parallel TASEP (2008)
  • Author(s): A. Borodin, P. L. Ferrari and T. Sasamoto
  • Journal Title: Comm. Math.Phys 283 Pages: 417-449
  • Peer Reviewed
• [Journal Article] Correlation function of the Schur process with a fixed final partition (2008)
  • Author(s): T. Imamura and T. Sasamoto
  • Journal Title: J. Math. Phys 49 Pages: 53302-53302
  • Peer Reviewed
• [Journal Article] Exact results for the 1D asymmetric exclusion process and KPZ fluctuations (2008)
  • Author(s): T. Sasamoto
  • Journal Title: Eur. Phys. Jour. B 64 Pages: 373-377
  • Peer Reviewed
• [Journal Article] Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition (2007)
  • Author(s): T. Imamura, T. Sasamoto
  • Journal Title: J. Stat. Phys. 128 Pages: 799-846
  • Peer Reviewed
• [Journal Article] (2007)
  • Author(s): A. Borodin, P.L. Ferrari, M. Praehofer, T. Sasamoto
  • Journal Title: J. Stat. Phys. 129 Pages: 1055-1080
  • Peer Reviewed
• [Journal Article] Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques (2007)
  • Author(s): T. Sasamoto
  • Journal Title: J. Stat. Mech.
  • Peer Reviewed
• [Journal Article] Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition (2007)
  • Author(s): T. Imamura and T. Sasamoto
  • Journal Title: J. Stat. Phys. 128 Pages: 799-846
  • Peer Reviewed
• [Journal Article] Fluctuation properties of the TASEP with periodic initial condition (2007)
  • Author(s): A. Borodin, M. Praehofer, P.L. Ferrari, T. Sasamoto
  • Journal Title: J. Stat. Phys. 129 Pages: 1055-1080
  • Peer Reviewed
• [Journal Article] Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques (2007)
  • Author(s): T. Sasamoto
  • Journal Title: J. Stat. Mech Pages: 7007-7007
  • Peer Reviewed
• [Presentation] GUEダイソンブラウン運動の最大値の分布について (2010)
  • Author(s): 笹本智弘
  • Organizer: 日本物理学会第65回年次大会
  • Place of Presentation: 岡山大学
• [Presentation] ダイソンブラウン運動の最大値の分布について (2010)
  • Author(s): 笹本智弘
  • Organizer: 日本数学会, 2010年年会
  • Place of Presentation: 慶応大学
• [Presentation] The dynamics of a tagged particle in 1D TASEP (2009)
  • Author(s): T. Sasamoto
  • Organizer: Aggregation, condensation and coagulation in particle systems
  • Place of Presentation: University of Warwick, UK
• [Presentation] Dynamics of a tagged particle in infinite TASEP (2009)
  • Author(s): T. Sasamoto
  • Organizer: Many-body systems far from equilibrium: Fluctuations, slow dynamics and long-range interactions
  • Place of Presentation: Max-Planck Institute Dresden, Germany
• [Presentation] An analysis of lattice KPZ equation (2009)
  • Author(s): T. Sasamoto, H. Spohn
  • Organizer: Workshop on Open Systems: Non-Equilibrium Phenomena - Dissipation, Decoherence, Transport, ETH Zurich
  • Place of Presentation: Switzerland
• [Presentation] Lattice KPZ equation (2009)
  • Author(s): T. Sasamoto, H. Spohn
  • Organizer: Scaling Limits in Models of Statistical Mechanics, Mathematisches Forschungsinstitut Oberwolfach
  • Place of Presentation: Germany
• [Presentation] On the maximum of Dyson Brownian motion (2009)
  • Author(s): T. Sasamoto
  • Organizer: 研究集会「大規模相互作用系の確率解析」
  • Place of Presentation: 東京大学数理
• [Presentation] 1D ASEP & KPZ (2009)
  • Author(s): 笹本智弘
  • Organizer: 研究集会「非線形波動研究の現状と将来-次の10年への展望」
  • Place of Presentation: 九州大学応用力学研究所
• [Presentation] Lattice KPZ equation (2009)
  • Author(s): T.Sasamoto, H.Spohn
  • Organizer: Scaling limits in models of statistical mechanics
  • Place of Presentation: Oberwolfach ドイツ
• [Presentation] The fluctuations of a tagged particle in one-dimensional exclusion process (2008)
  • Author(s): T. Sasamoto
  • Organizer: Random Tilings, Random Partitions and Stochastic Growth Processes
  • Place of Presentation: モントリオール大学数学研究所
  • Year and Date: 2008-09-05
• [Presentation] Dynamics of a tagged particle in one-dimensional exclusion process (2008)
  • Author(s): T. Sasamoto
  • Organizer: Workshop on Stochastic Eigen-Analysis (Random Matrices)
  • Place of Presentation: Hong Kong
• [Presentation] The fluctuations of a tagged particle in one-dimensional exclusion process (2008)
  • Author(s): T. Sasamoto
  • Organizer: Random Tilings, Random Partitions and Stochastic Growth Processes
  • Place of Presentation: ontreal, Canada
• [Presentation] 非平衡定常系の模型の厳密解 (2008)
  • Author(s): 笹本智弘
  • Organizer: 日本物理学会第62回年次大会
  • Place of Presentation: 近畿大学
• [Presentation] 可積分系の手法を用いた1次元確率的無限粒子系の解析 (2008)
  • Author(s): 笹本智弘
  • Organizer: 日本数学会
  • Place of Presentation: 近畿大学
• [Presentation] 2種類の速さを持つ1次元非対称排他過程の粒子の位置の揺らぎ (2008)
  • Author(s): 笹本智弘
  • Organizer: 日本物理学会, 2008年秋季大会
  • Place of Presentation: 岩手大学
• [Presentation] Particle Position Fluctuations in the Asymmetric Exclusion Process (2007)
  • Author(s): T. Sasamoto
  • Organizer: International Meeting on Perspectives of Soliton Physics
  • Place of Presentation: Tokyo, Japan
• [Presentation] Determinantal structure of the 1D asymmetric exclusion process and KPZ fluctuations (2007)
  • Author(s): T. Sasamoto
  • Organizer: STATPHYS23
  • Place of Presentation: Genova, Italy
• [Presentation] Fluctuations of the 1D KPZ surface with flat initial conditions (2007)
  • Author(s): T. Sasamoto
  • Organizer: Fluctuation and dissipation phenomena in driven systems far from equilibrium
  • Place of Presentation: Dresden, Germany
• [Presentation] The fluctuations of the polynuclear growth model with flat initial conditions (2007)
  • Author(s): T. Sasamoto
  • Organizer: Stochastic Analysis on Large Scale Interacting Systems
  • Place of Presentation: Fukuoka, Japan
• [Presentation] 非平衡統計力学×確率モデル×厳密解=ASEP (2007)
  • Author(s): 笹本智弘
  • Organizer: 日本物理学会2007年秋季大会
  • Place of Presentation: 北海道大学
• [Presentation] On the transitions between the GOE and GUE Tracy-Widom distributions (2007)
  • Author(s): 笹本智弘
  • Organizer: 研究集会「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
• [Presentation] 1次元多核成長模型の揺らぎ (2007)
  • Author(s): 笹本智弘
  • Organizer: 「結晶成長の数理」第二回研究会
  • Place of Presentation: 学習院大学
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~sasamoto/
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~sasamoto
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~sasamoto
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~sasamoto/