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Interacting urns on directed networks with node-dependent sampling and reinforcement

Part of: Operations research and management science Limit theorems Special processes

Published online by Cambridge University Press:  03 February 2025

Gursharn Kaur  and
Neeraja Sahasrabudhe
Gursharn Kaur*
Affiliation:
University of Virginia
Neeraja Sahasrabudhe*
Affiliation:
Indian Institute of Science Education and Research
*
*Postal address: Biocomplexity Institute, University of Virginia, Charlottesville, USA. 22904. Email: [email protected]
**Postal address: Department of Mathematical Sciences, IISER Mohali, Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306, India. Email: [email protected]
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Abstract

We consider interacting urns on a finite directed network, where both sampling and reinforcement processes depend on the nodes of the network. This extends previous research by incorporating node-dependent sampling and reinforcement. We classify the sampling and reinforcement schemes, as well as the networks on which the proportion of balls of either colour in each urn converges almost surely to a deterministic limit. We also investigate conditions for achieving synchronisation of the colour proportions across the urns and analyse fluctuations under specific conditions on the reinforcement scheme and network structure.

Keywords

Reinforcementstochastic approximationcentral limit theoremsynchronisation

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60F05: Central limit and other weak theorems 90B15: Network models, stochastic
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 25
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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