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2003 Fiscal Year Final Research Report Summary

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
KeywordsInteracting particle systems / Contact Process / duality / correlation inequality / quantum random walk / phase transition
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.

  • Research Products

    (9 results)

All Other

All Publications (9 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 2005-04-19  

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