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Asymptotic results of a multiple-entry reinforcement process
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Alves, Caio, Ribeiro, Rodrigo and Valesin, Daniel (2023) Asymptotic results of a multiple-entry reinforcement process. Stochastic Processes and their Applications, 161 . pp. 451-489. doi:10.1016/j.spa.2023.03.010 ISSN 0304-4149.
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Official URL: http://doi.org/10.1016/j.spa.2023.03.010
Abstract
We introduce a class of stochastic processes with reinforcement consisting of a sequence of random partitions, where is a partition of
. At each time numbers are added to the set being partitioned; of these, a random subset (chosen according to a time-dependent probability distribution) joins existing blocks, and the others each start new blocks on their own. Those joining existing blocks each choose a block with probability proportional to that block’s cardinality, independently. We prove results concerning the asymptotic cardinality of a given block and central limit theorems for associated fluctuations about this asymptotic cardinality: these are proved both for a fixed block and for the maximum among all blocks. We also prove that with probability one, a single block eventually takes and maintains the leadership in cardinality. Depending on the way one sees this partition process, one can translate our results to Balls and Bins processes, Generalized Chinese Restaurant Processes, Generalized Urn models and Preferential attachment random graphs.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Stochastic processes, Random walks (Mathematics), Random graphs, Reinforcement (Psychology) | |||||||||
Journal or Publication Title: | Stochastic Processes and their Applications | |||||||||
Publisher: | Elsevier Science BV | |||||||||
ISSN: | 0304-4149 | |||||||||
Official Date: | July 2023 | |||||||||
Dates: |
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Volume: | 161 | |||||||||
Page Range: | pp. 451-489 | |||||||||
DOI: | 10.1016/j.spa.2023.03.010 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 20 July 2023 | |||||||||
Date of first compliant Open Access: | 3 April 2024 | |||||||||
RIOXX Funder/Project Grant: |
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