论文标题
稳定的Derrida-关键的Retaux系统
The stable Derrida--Retaux system at criticality
论文作者
论文摘要
Derrida和Retaux（2014）研究了Derrida - Retaux递归系统，作为统计物理学中的层次重归化模型。 Derrida和Retaux（2014）对自由能的预测最近已被严格证明（Chen，Dagard，Derrida，Hu，Lifshits and Shi（2019+），证实了Berezinskii--kosterlitz-- kosterlitz--在系统中无效的型相变。有趣的是，它是在Chen，Dagard，Derrida，Hu，Lifshits and Shi（2019+）中建立的，即仅在初始分布的某个集成性假设下进行预测有效，并且当不满足这种可集成性假设时已显示出新的普遍性结果。我们提出了一种满足特定统治条件的系统的统一方法，并为当时生成函数的所有顺序提供了上限。当不满足可集成性假设时，我们的结果允许确定在关键时刻生成函数的矩乘积的大数量级，确认并完成了Collet，Eckmann，Eckmann，Glaser和Martin（1984）的先前结果。
The Derrida--Retaux recursive system was investigated by Derrida and Retaux (2014) as a hierarchical renormalization model in statistical physics. A prediction of Derrida and Retaux (2014) on the free energy has recently been rigorously proved (Chen, Dagard, Derrida, Hu, Lifshits and Shi (2019+)), confirming the Berezinskii--Kosterlitz--Thouless-type phase transition in the system. Interestingly, it has been established in Chen, Dagard, Derrida, Hu, Lifshits and Shi (2019+) that the prediction is valid only under a certain integrability assumption on the initial distribution, and a new type of universality result has been shown when this integrability assumption is not satisfied. We present a unified approach for systems satisfying a certain domination condition, and give an upper bound for derivatives of all orders of the moment generating function. When the integrability assumption is not satisfied, our result allows to identify the large-time order of magnitude of the product of the moment generating functions at criticality, confirming and completing a previous result in Collet, Eckmann, Glaser and Martin (1984).
