Understanding how knowledge emerges and propagates within groups is crucial to explain the evolution of human populations. In this work, we introduce a mathematically oriented model that draws on individual-based approaches, inhomogeneous Markov chains and learning algorithms, such as those introduced in [F. Cucker and S. Smale, On the mathematical foundations of learning, Bull. Amer. Math. Soc. 39 (2002) 1–49; F. Cucker, S. Smale and D. X. Zhou, Modeling language evolution, Found. Comput. Math. 4 (2004) 315–343]. After deriving the model, we study some of its mathematical properties, and establish theoretical and quantitative results in a simplified case. Finally, we run numerical simulations to illustrate some properties of the model. Our main result is that, as time goes to infinity, individuals’ knowledge can converge to a common shared knowledge that was not present in the convex combination of initial individuals’ knowledge.

中文翻译：

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具有人口结构、社会学习和可信度偏差的随机文化进化模型中的知识收敛

了解知识如何在群体中出现和传播对于解释人口的进化至关重要。在这项工作中，我们介绍了一个面向数学的模型，该模型利用了基于个体的方法、非同质马尔可夫链和学习算法，例如 [F. Cucker 和 S. Smale，关于学习的数学基础，Bull。阿米尔。数学。社会党。39 (2002) 1-49；F. Cucker、S. Smale 和 DX Zhou，建模语言进化，发现。计算。数学。4 (2004) 315–343]。在推导模型之后，我们研究了它的一些数学性质，并在简化的情况下建立了理论和定量结果。最后，我们运行数值模拟来说明模型的一些特性。我们的主要结果是，随着时间的流逝，