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Study on phase transition for interacting particle systems

Research Project

Project/Area Number 12440024
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionYokohama National University

Principal Investigator

KONNO Norio  Yokohama National University, Faculty of Engineering, Associate Professor, 工学研究院, 助教授 (80205575)

Co-Investigator(Kenkyū-buntansha) HIRANO Norimichi  Yokohama National University, Faculty of Environment and Information, Sciences Professor, 環境情報研究院, 教授 (80134815)
TAKANO Seiji  Yokohama National University, Faculty of Engineering, Professor, 工学研究院, 教授 (90018060)
UKAI Seiji  Yokohama National University, Faculty of Engineering, Professor, 工学研究院, 教授 (30047170)
SAITO Noriko  Yokohama National University, Faculty of Environment and Information, Associate Professor, 工学研究院, 助手 (50175353)
Project Period (FY) 2000 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥15,300,000 (Direct Cost: ¥15,300,000)
Fiscal Year 2003: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2002: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2001: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2000: ¥3,900,000 (Direct Cost: ¥3,900,000)
KeywordsInteracting particle systems / Contact Process / duality / correlation inequality / quantum random walk / phase transition / パーコレーション / 極限定理 / コンタクトプロセス
Research Abstract

We study phase transitions of interacting particle systems, in particular, contact process type model, the Domany-Kinzel model by using various correlation inequalities and correlation identities. Recently we obtain the BFKL inequality which is a refinement of a special case of the well-known Harris-FKG inequality. From this inequality, bounds of the survival probability and critical value can be obtained systematically. In general, we can apply the above mentioned method (called correlation inequality method (CIM) to attractive interacting particle systems. However it was not known whether or not the CIM can be applied to even non-attractive models. Some Monte Carlo simulations suggested that some non-attractive models satisfy the Harris-FKG type inequality. In fact, we could prove this fact later. But we do not show that the BFKL inequality can be satisfied for the same model. Furthermore we obtain a necessary and sufficient condition on duality for the Domany-Kinzel model by several methods. One of them is closely related to quantum mechanics. So we move to study quantum walks which have been widely studied in the field of quantum computing. In particular, we study symmetry of distribution, limit theorems, and absorption problems of quantum walks with nearest-neighbor transition in one dimension. Very recently we show a localization of two-dimensional quantum walk including the Grover walk.

Report

(5 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (28 results)

All Other

All Publications (28 results)

  • [Publications] N.Konno: "Absorption problems for quantum walks in one dimension"J.Phys.A : Math.Gen.. 36. 241-253 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 今野 紀雄: "確立セルオートマトンの数理構造"数理科学. 483. 43-49 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Konno: "Symmetry of distribution for the one-dimensional Hadamand Walk"Inter disciplinary Information Sciences. 10. 11-22 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 今野 紀雄: "量子ウォークの極限定理"数理科学. 492. 37-44 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Kono: "Coexistence results for a spatial stochastic eppidemic model"Markov Process.Related Fields. (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 今野 紀雄: "コンタクト・プロセスの相転移現象"横浜図書. 112 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Konno: "Absorption problems for quantum walks in one dimension"J.Phys.A : Math.Gen. 36. 241-253 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Konno: "Symmetry of distribution for the one-dimensional Hadamand walk"Interdisciplinary Information Sciences. 10. 11-22 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Konno: "Coexistence results for a spatial stochastic epidemic model"Markor Process.Refated Fields. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Konno, T.Namiki, T.Soshi, A.Sudburg: "Absorption problems for quantum random walks in one dimertion"Journal of Physics A : Mathematical and General. 36巻. 241-253 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Konno, T.Namiki, T.Soshi: "Symmetry of Distribution for the One-Dimensional Hadaward Walk"Interdisciplinarg Information Sciences. 10巻1号. 11-22 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Katori, N.Konno, A.Sudburg, H.Tanemura: "Dualities for the Domang-Kinzel model"Journal of Theuretical Probability. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Konno, R.Schinazi, H.Tanemura: "Coexistence results for a spatial stochastic epidemic model"Markov Processes and Related Fields. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Masuda, N.Konno: "Return times of random walks on generalized random graphs"Physical Review E. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Masuda, N.Konno, K.Aihara: "Transmission of SARS in dynamical small-world networks"Physical Review E. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Norio Konno: "Limit theorems and absorption problems for quantum random walks in one dimension"Quantum Information and Computation. Vol.2. 578-595 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Norio Konno: "Quantum random walks in one dimension"Quantum Information Processing. Vol.1. (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Norio Konno, Takao Namiki, Takahiro Soshi, Aidan Sadbury: "Absorption problems for quantum walks in one dimension"Journal of Physics A : Mathematical and General. Vol.36. 241-253 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sarato Takahashi: "On some Harris-FKG type correlation inequalities for a non-attractive model"Journal of Statistical Physics. Vol.102, Nos.5/6. 1429-1438 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kazunori Sato: "Parity law for population dynamics of N-species wity cyclic advantage competitions"Applied Mathematics and Computation. Vol.126 Nos.2-3. 255-270 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Norio Konno: "Dualities for a class of finite range probabilistic cellular automata"Journal of Statistical Physics. Vol.106 No.5. 915-922 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Norio Konno: "Self-duality for multi-state probabilistic cellular automata with finite range interactions"Journal of Statistical Physics. Vol.106 No.5. 923-930 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Seiji Ukai: "The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem"Japan Journal of Industrial and Applied Mathematics. Vol.18 No.2. 383-392 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 今野 紀雄: "コンタクト・プロセスの相転移現象-相関不等式法とハリスの補題法-"横浜図書. 113 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Norio Konno: "Lower bounds for critical values of a cancellatine model"Journal of Physics A : Mathematical and General. 33. 319-326 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Makoto Katori: "Survival probabilities for discrete-time models in one dimension"Journal of Statistical Physics. 99. 603-612 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Makoto Katori: "Extension of the Arrowsmith-Essam formula to the Domany-Kinzel model"Journal of Statistical Physics. 101. 747-774 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Norio Konno: "Dualities for discrete-time stochastic models in one dimension"Transactions of Materials Research Society of Japan. 26. (2001)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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