Infinite particle systems of long range jumps with long range interactions
Infinite particle systems of long range jumps with long range interactions
复制标题
具有长程相互作用的长程跳跃的无限粒子系统
DOI：
10.2748/tmj/1552100440
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发表时间：
2015
影响因子：
0.5
通讯作者：
Syota Esaki
中科院分区：
文献类型：
--
作者：
Syota Esaki
本文提出了构造具有长程相互作用的跳跃型无限粒子系统的一般定理。它可以应用于每个粒子都经历$\alpha$稳定过程的系统，粒子之间的相互作用由随机矩阵理论的对数势或多项式衰减的Ruelle类势给出。结果表明，对于 (0, 2)$ 中的任意 $\alpha \in (0, 2)$，如果其均衡测度 $\mu$ 具有平移不变性，并且一般情况下 $\alpha$ 受测度 $\mu$ 的 1-相关函数的增长阶数限制，则可以构造系统。
In this paper a general theorem of constructing infinite particle systems of jump types with long range interactions is presented. It can be applied to the system that each particle undergoes an $\alpha$-stable process and interaction between particles is given by the logarithmic potential appearing random matrix theory or potentials of Ruelle's class with polynomial decay. It is shown that the system can be constructed for any $\alpha \in (0, 2)$ if its equilibrium measure $\mu$ is translation invariant, and $\alpha$ is restricted by the growth order of the 1-correlation function of the measure $\mu$ in general case.