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

基本信息

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

项目摘要

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平等的相互作用粒子系统（IPS），例如Harris-Fkg不平等，表现性和BFKL不等式。特别是，BFKL不平等是一种新型的相关性不平等，也是Harris-Fkg不平等和副二的不平等现象。作为IPSS的典型示例，我们在这里关注一维接触过程。通过使用上述相关性不平等，与其他方法相比，我们可以轻松而系统地获得较低的键和临界范围的键，即接触过程的生存概率，即边缘工艺技术和Harris引理方法。因此，我们称此方法相关性不等式方法。但是，目前阶段的方法存在一些局限性，接触过程很有吸引力和两国过程。因此，我们正在研究Harris-FKG不平等和/或BFKL不平等是否是否在非吸引力和/或多种状态IPS中也存在。关于非吸引力的Domany-Kinzel模型，蒙特 - 卡洛模拟表明Harris-FKG不等式是正确的。在某些特殊情况下，我们可以证明它最近成立。对于多状态IPS，例如，根据Monte-Carlo模拟的结果，Harris-FKG类型不等式和BFKL型不等式和BFKL型不等式和BFKL型不平等和BFKL型不等式都正确。