作为创新简单模型的交互分支过程
The Interacting Branching Process as a Simple Model of Innovation
摘要：
我们用广义分支过程来描述创新。每一项新发明与任何现有发明配对，产生一定数量的后代，这些后代是泊松分布的，平均值为p。现有发明在每一代的死亡概率为p/τ。与平均场结果相反，没有发生相变;对于所有p > 0，存活的机会是有限的。当τ= \infty时，幸存的过程在超指数增长之前会出现瓶颈--这种增长符合加速回报的规律。这种行为对于有限的τ仍然存在。我们详细分析了p \to 0时的渐近行为。
英文摘要：
We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/τat each generation. In contrast to mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For τ= \infty, surviving processes exhibit a bottleneck before exploding super-exponentially - a growth consistent with a law of accelerating returns. This behavior persists for finite τ. We analyze, in detail, the asymptotic behavior as p \to 0.
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