Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases
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7 décembre 2020
- ISIDORE Id: 10670/1.a65b14...
- hal: hal-02357188
- ARXIV: 1911.05482
- doi: 10.1142/S0218202520500529
Ce document est lié à :
info:eu-repo/semantics/altIdentifier/arxiv/1911.05482
Ce document est lié à :
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202520500529
Ce document est lié à :
info:eu-repo/grantAgreement//748310 /EU/Experimental Programme Investigating Cumulative Culture/EPICC
info:eu-repo/semantics/OpenAccess
Mots-clés
language evolution inhomogeneous Markov chains concentration inequalities numerical simulations convergence to equilibrium Individual based model cultural evolution cumulative culture 92D25, 68T05, 92H10.Citer ce document
Sylvain Billiard et al., « Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases », HAL SHS (Sciences de l’Homme et de la Société), ID : 10.1142/S0218202520500529
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Résumé
Understanding how knowledge is created and propagates within groups is crucial to explain how human populations have evolved through time. Anthropologists have relied on different theoretical models to address this question. In this work, we introduce a mathematically oriented model that shares properties with individual based approaches, inhomogeneous Markov chains and learning algorithms, such as those introduced in [F. Cucker, S. Smale, Bull. Amer. Math. Soc, 39 (1), 2002] and [F. Cucker, S. Smale and D. X Zhou, Found. Comput. Math., 2004]. 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.
