论文标题
投票模型和半连接抛物线方程
Voting models and semilinear parabolic equations
论文作者
论文摘要
我们以多项式非线性的方式对解决方案的解决方案的解决方案提出了概率的解释，该方程在分支布朗尼运动（BBM）的家谱树上的投票模型方面具有多项式非线性。这些扩展了McKean在〜\ cite {McK}中发现的Fisher-KPP方程与BBM之间的连接。特别是，我们提出``随机结果''和``随机阈值''投票模型，这些模型产生了满足$ f（0）= f（0）= 0 $的多项式非线性$ f $ f $ f $ f $ f（1）= 0 $，并且``递归''递归增强了树模型，从而超出了$ f $的限制。我们计算了一些特别感兴趣的例子；例如，我们根据非平凡的投票模型和``基于群体''的投票规则获得了对热方程式的奇怪解释，该规则导致对Ephmi-Pullyu过渡的概率观点，以埃伯特（Eber）和范·萨拉卢斯（van Saarloos）引入一类非线性。
We present probabilistic interpretations of solutions to semi-linear parabolic equations with polynomial nonlinearities in terms of the voting models on the genealogical trees of branching Brownian motion (BBM). These extend the connection between the Fisher-KPP equation and BBM discovered by McKean in~\cite{McK}. In particular, we present ``random outcome'' and ``random threshold'' voting models that yield any polynomial nonlinearity $f$ satisfying $f(0)=f(1)=0$ and a ``recursive up the tree'' model that allows to go beyond this restriction on $f$. We compute a few examples of particular interest; for example, we obtain a curious interpretation of the heat equation in terms of a nontrivial voting model and a ``group-based'' voting rule that leads to a probabilistic view of the pushmi-pullyu transition for a class of nonlinearities introduced by Ebert and van Saarloos.
