论文标题
合并方程的临界行为和缩放函数
The critical behaviors and the scaling functions of a coalescence equation
论文作者
论文摘要
我们表明，结合方程式表现出各种关键行为，具体取决于初始条件。几年前引入了该方程式，以了解一种玩具模型（由德里达（Derrida）和retaux研究以模仿存在疾病的过渡。最近显示，该玩具模型表现出与当前工作中研究的方程式相同的关键行为。在这里，我们发现了几个合并方程的精确解决方案的家族，特别是与不同可能的关键行为密切相关的缩放函数系列。这些缩放函数导致了新的猜想，特别是在临界树的形状上，我们已经检查了数值。
We show that a coalescence equation exhibits a variety of critical behaviors, depending on the initial condition. This equation was introduced a few years ago to understand a toy model {studied by Derrida and Retaux to mimic} the depinning transition in presence of disorder. It was shown recently that this toy model exhibits the same critical behaviors as the equation studied in the present work. Here we find several families of exact solutions of this coalescence equation, in particular a family of scaling functions which are closely related to the different possible critical behaviors. These scaling functions lead to new conjectures, in particular on the shapes of the critical trees, that we have checked numerically.
