Varadhan's Decomposition of Shift-Invariant Closed $L^2$-forms for Large Scale Interacting Systems on the Euclidean Lattice
Varadhan's Decomposition of Shift-Invariant Closed $L^2$-forms for Large Scale Interacting Systems on the Euclidean Lattice
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欧几里德格子上大规模交互系统的平移不变封闭 $L^2$ 形式的 Varadhan 分解
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
M. Sasada
中科院分区：
文献类型：
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作者：
Kenichi Bannai;M. Sasada
我们严格地制定并证明了欧几里德晶格（Z，E）上大规模相互作用系统的相对一般的相互作用类别 Varadhan 的平移不变闭合 !-形式的分解。这种封闭形式的分解在证明非梯度系统的扩散标度极限方面发挥了重要作用。守恒量的普遍表达是从特定模型的观察中寻找的，但迄今为止，精确的公式或严格的证明还难以实现。我们的结果基于我们在上一篇文章 [1] 中研究的平移不变闭合一致形式的通用分解。在本文中，我们表明相同的通用结构也出现在 !-形式中。基本假设是：（i）每个顶点上的状态集是有限集，（ii）配置空间上的测量是乘积测量，以及（iii）对于相互作用的平均场版本存在一定的统一谱间隙估计。我们的结果适用于广义排除过程、多物种排除过程和更一般的晶格气体模型。
We rigorously formulate and prove for a relatively general class of interactions Varadhan’s Decomposition of shift-invariant closed !-forms for a large scale interacting system on a Euclidean lattice (Z, E). Such decomposition of closed forms has played an essential role in proving the diffusive scaling limit of nongradient systems. The universal expression in terms of conserved quantities was sought from observations for specific models, but a precise formulation or rigorous proof up until now had been elusive. Our result is based on the universal decomposition of shift-invariant closed uniform forms studied in our previous article [1]. In the present article, we show that the same universal structure also appears for !-forms. The essential assumptions are: (i) the set of states on each vertex is a finite set, (ii) the measure on the configuration space is the product measure, and (iii) there is a certain uniform spectral gap estimate for the mean field version of the interaction. Our result is applicable for generalized exclusion processes, multi-species exclusion processes, and more general lattice gas models.
晶格中排斥过程的流体力学极限
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发表时间：
2011
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作者：
Masaki Inoue;Teruyo Wada;Masao Ikeda;Eiho Uezato;田中亮吉;井上正樹;井上正樹;Ryokichi Tanaka;Masaki INOUE;田中亮吉;Ryokichi Tanaka
通讯作者：
Ryokichi Tanaka
两种物质排除过程的流体动力学极限
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发表时间：
2008
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作者：
Y. Ohyama;T. Onaka (2 番目);I. Sakon (7 番目);Y. Ita (11 番目);T. Tanabe (16 番目);他20名;舟木直久
通讯作者：
舟木直久
非简谐振子链的宏观能量扩散，Stefano Olla
影响因子：
2
作者：
Garcia-Marin;M.;et al.;Tokuji Araya; Kei-ichiro Iima; Ryo Takahashi;大城佳奈子;Makiko SASADA
通讯作者：
Makiko SASADA