强关联多体经典系统的特殊概率行为
Paradoxical probabilistic behavior for strongly correlated many-body classical systems
摘要：
利用一个简单的概率模型，我们说明了一个强关联多体经典系统的一小部分可以表现出一种悖论行为，即渐近随机独立性。我们考虑一个三角形数组，使得每一行都是$n$强相关随机变量的列表。即使当$n\to\infty$时，相关性也被保留，因为标准的中心极限定理对该阵列不成立。我们证明，如果我们选择一个固定数量的随机变量的$m<n$第行和跟踪其他$n-m$变量，然后考虑$n\to\infty$，$m$选择的，矛盾的是，原来是独立的。但是，如果$m$随着$n$的增加而增加，情况可能会有所不同。最后，我们提出了一个可能的实验验证我们的结果附近的临界的二阶相变。
英文摘要：
Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that each row is a list of $n$ strongly correlated random variables. The correlations are preserved even when $n\to\infty$, since the standard central limit theorem does not hold for this array. We show that, if we choose a fixed number $m<n$ of random variables of the $n$th row and trace over the other $n-m$ variables, and then consider $n\to\infty$, the $m$ chosen ones can, paradoxically, turn out to be independent. However, the scenario can be different if $m$ increases with $n$. Finally, we suggest a possible experimental verification of our results near criticality of a second-order phase transition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
