期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 30, 期 14, 页码 2691-2723出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202520500529
关键词
Individual-based model; inhomogeneous Markov chains; convergence to equilibrium; numerical simulations; concentration inequalities; cultural evolution; language evolution; cumulative culture
资金
- chair Modelisation Mathematique et Biodiversite of Veolia Environnement-Ecole Polytechnique-Museum National d'Histoire NaturelleFondation X
- European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie Grant Agreement [748310]
- ANR [ANR-17EURE-0010]
- ANR SUPERGENE [ANR-18-CE02-0019]
- Labex CEMPI [ANR-11-LABX-0007-01]
- ANR Project MoHyCon [ANR-17-CE40-0027-01]
- Agence Nationale de la Recherche (ANR) [ANR-18-CE02-0019] Funding Source: Agence Nationale de la Recherche (ANR)
- Marie Curie Actions (MSCA) [748310] Funding Source: Marie Curie Actions (MSCA)
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.
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