Simple proof demonstrates maintained color dominance in Pólya urns under specific conditions.
Consider a Pólya urn where a drawn ball of colour i is replaced together with a fixed number mᵢ of balls of the same colour. We give a simple proof that if, for example, there are two colours and the urn starts with more balls of colour 1 than 2, and m₁≥ m₂, then there is a positive probability that there always will be more balls of colour 1 than colour 2.
No takes yet. Share an insight, caveat, or question.
Svante Janson (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: