The Urn of Hill, Lane and Sudderth

2025/06/25 by Franchini, Simone
#91B02 #91B42 #91B82 #FOS: Mathematics #G.3 #I.6 #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.20826

Abstract

We review some facts, properties and applications of the urn of Hill, Lane and Sudderth, a paradigmatic model of stochastic process with memory where the urn evolution is as follows: consider an urn of given capacity, at each step a new ball, black or white, is added to the urn with probability that is function (urn function) of the fraction of black balls. The process runs until capacity is reached.

Citations

• Elephant random walks with multiple extractions and general reinforcement functions
• Elephant Random Walk with multiple extractions
• Catene ideali con numero fissato di auto-intersezioni
• Fixation of leadership in non-Markovian growth processes
• The marginal majority effect: when social influence produces lock-in
• Asymptotic Properties of Generalized Elephant Random Walks
• Large Deviations Theory of Increasing Returns
• Energy of the Interacting Self-Avoiding Walk at the θ-point
• On the center of mass of the elephant random walk
• A free energy principle for a particular physics
• Random Polymers and Generalized Urn Processes
• One-to-one Mapping between Stimulus and Neural State: Memory and Classification
• Large deviations for Generalized Polya Urns with arbitrary urn function
• Exactly Solvable Balanced Tenable Urns with Random Entries via the Analytic Methodology
• Moderate deviations for the volume of the Wiener sausage
• Active Inference: A Process Theory

Related

• Functional central limit theorems for occupancies and missing mass\n process in infinite urn models
• Preferential Attachment When Stable
• Interacting Urn Models
• Urn models with two types of strategies
• Urns & Tubes