Analysis on Interacting Particle Systems Based on a New Type of Correlation Inequalities

基于新型相关不等式的相互作用粒子系统分析

• 批准号: 09640250
• 负责人: KONNO Norio
• 金额: $ 1.92万
• 依托单位: Yokohama National University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640250/
• 关键词: correlation inequality; interacting particle system; phase transition; contact process; percolation

We study interacting particle systems (IPSs) based on correlation inequalities, for examples, Harris-FKG inequality, submodularity, and BFKL inequality. In particular, BFKL inequality is a new type of correlation inequality and a refinement of Harris-FKG inequality and submodularity. As a typical example of IPSs, here we focus on one-dimensional contact process. By using above correlation inequalities, we can easily and systematically obtain lower bonds on critical value and upper bounds on survival probability of contact process, compared with other methods, i.e, edge process technique and Harris lemma method. So we call this method correlation inequality method. However there are some limitations on the method in the present stage, The contact process is attractive and two-state process. Therefore we are studying whether or not Harris-FKG inequality and/or BFKL inequality hold even in non-attractive and/or multi-sate IPSs. Concerning non-attractive Domany-Kinzel model, Monte-Carlo simulations suggest that Harris-FKG inequality is correct. For some special cases we could prove it holds very recently. As for multi-state IPSs, for example, 3-state cyclic particle system and successional model in two dimensions, both-Harris-FKG type inequality and BFKL type one would be correct according to results on Monte-Carlo simulations.

我们研究了基于相关不等式的相互作用粒子系统，如Harris-FKG不等式、子模块性和BFKL不等式。特别地，BFKL不等式是一类新的相关不等式，是Harris-FKG不等式和子模性的一个改进。作为IPS的一个典型例子，这里我们主要讨论一维接触过程。利用上述相关不等式，与其它方法（如边处理技术和Harris引理）相比，我们可以方便而系统地得到接触过程的临界值下界和生存概率上界.因此我们称这种方法为相关不等式法。但是，现阶段的方法存在一定的局限性，接触过程是一种有吸引力的两态过程。因此，我们正在研究是否Harris-FKG不等式和/或BFKL不等式成立，即使在非吸引和/或多状态IPS。对于非吸引Domany-Kinzel模型，蒙特-卡罗模拟结果表明Harris-FKG不等式是正确的.对于某些特殊情况，我们可以证明它最近成立。对于多状态IPS，如三状态循环粒子系统和二维连续模型，蒙特-卡罗模拟结果表明，Harris-FKG型不等式和BFKL型不等式都是正确的。

项目成果

Alex yu, Trefyakov, Norio Inui and Norio Konno: "Phase transition for the one-sided contact process"Journal of the Physical Society of Japan. 66. 3764-3769 (1997)

Alex yu、Trefyakov、Norio Inui 和 Norio Konno：“单侧接触过程的相变”日本物理学会杂志。

Masato Urano, Nori Konno and Kazuhori Sato: "Correlation inequalities for 3-state cyclic andvantage model"Proceedings of International workshop on Soft Computing in Industry '99. 78-82 (1999)

Masato Urano、Nori Konno 和 Kazuhori Sato：“三态循环和优势模型的相关不等式”99 年工业软计算国际研讨会论文集。

Norio Konno, Kazunori Sato and Aiden Sudbury: "Lower bounds for critical values of a cancellative model"Journal of Physics A. (2000)

Norio Konno、Kazunori Sato 和 Aiden Sudbury：“取消模型临界值的下限”Journal of Chemistry A. (2000)

Tetsuhiro Nagamura, Vladimir Belitsky, Norio Konno and Tadashi Yamaguchi: "Upper bounds on percolation probabilities for oriented bond percelation"Memoirs of the Muroran Institute of Technology. 47. 115-121 (1997)

Tetsuhiro Nagamura、Vladimir Belitsky、Norio Konno 和 Tadashi Yamaguchi：“定向键渗透的渗透概率上限”室兰工业学院回忆录。

Masato Urano: "Clustering and Coexistence for Long Range Cyclic Advantage Mode in One Dimensity" Proceedings of International Workshop on Soft Compating in Industry'99. (1999)

Masato Urano：“一维长程循环优势模式的聚类与共存”工业软计算国际研讨会论文集99。