Publication:

Reinforced Galton–Watson processes I: Malthusian exponents

Date

Date

Date
2024
Journal Article
Published version
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cris.lastimport.scopus2025-06-26T03:31:40Z
cris.lastimport.wos2025-07-30T01:30:34Z
dc.contributor.institutionUniversity of Zurich
dc.date.accessioned2024-05-09T10:23:43Z
dc.date.available2024-05-09T10:23:43Z
dc.date.issued2024-09-01
dc.description.abstract

In a reinforced Galton–Watson process with reproduction law and memory parameter , the number of children of a typical individual either, with probability , repeats that of one of its forebears picked uniformly at random, or, with complementary probability , is given by an independent sample from . We estimate the average size of the population at a large generation, and in particular, we determine explicitly the Malthusian growth rate in terms of and . Our approach via the analysis of transport equations owes much to works by Flajolet and co‐authors.

dc.identifier.doi10.1002/rsa.21219
dc.identifier.issn1042-9832
dc.identifier.scopus2-s2.0-85191159297
dc.identifier.urihttps://www.zora.uzh.ch/handle/20.500.14742/219207
dc.identifier.wos001205998000001
dc.language.isoeng
dc.subjectGalton-Watson process
dc.subjectMalthusian growth exponent
dc.subjectsingularity analysis of generating functions
dc.subjectstochastic reinforcement
dc.subjecttransport equation Research Areas
dc.subjectComputer Science
dc.subjectMathematics Computer Science
dc.subjectSoftware EngineeringMathematics
dc.subjectAppliedMathematics
dc.subject.ddc510 Mathematics
dc.title

Reinforced Galton–Watson processes I: Malthusian exponents

dc.typearticle
dcterms.accessRightsinfo:eu-repo/semantics/openAccess
dcterms.bibliographicCitation.journaltitleRandom Structures & Algorithms
dcterms.bibliographicCitation.number2
dcterms.bibliographicCitation.originalpublishernameWiley-Blackwell Publishing, Inc.
dcterms.bibliographicCitation.pageend410
dcterms.bibliographicCitation.pagestart387
dcterms.bibliographicCitation.volume65
dspace.entity.typePublicationen
uzh.contributor.affiliationUniversity of Zurich
uzh.contributor.affiliationInstitut de Mathématiques de Toulouse
uzh.contributor.authorBertoin, Jean
uzh.contributor.authorMallein, Bastien
uzh.contributor.correspondenceNo
uzh.contributor.correspondenceYes
uzh.document.availabilitypublished_version
uzh.eprint.datestamp2024-05-09 10:23:43
uzh.eprint.lastmod2025-07-30 01:35:23
uzh.eprint.statusChange2024-05-09 10:23:43
uzh.harvester.ethYes
uzh.harvester.nbNo
uzh.identifier.doi10.5167/uzh-259472
uzh.jdb.eprintsId17235
uzh.note.publicACKNOWLEDGMENTS We express our sincere gratitude to the reviewers for their insightful comments, which greatly contributed to enhancing the quality of this manuscript. J.B. would also like to thank KlausWidmayer for discussions about transport equations, and notably Lemma 3.3. DATA AVAILABILITY STATEMENT Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
uzh.oastatus.unpaywallhybrid
uzh.oastatus.zoraHybrid
uzh.publication.citationBertoin, Jean; Mallein, Bastien (2024). Reinforced Galton–Watson processes I: Malthusian exponents. Random Structures & Algorithms, 65(2):387-410.
uzh.publication.originalworkoriginal
uzh.publication.publishedStatusfinal
uzh.scopus.impact1
uzh.scopus.subjectsSoftware
uzh.scopus.subjectsGeneral Mathematics
uzh.scopus.subjectsComputer Graphics and Computer-Aided Design
uzh.scopus.subjectsApplied Mathematics
uzh.workflow.doajuzh.workflow.doaj.false
uzh.workflow.eprintid259472
uzh.workflow.fulltextStatuspublic
uzh.workflow.revisions40
uzh.workflow.rightsCheckkeininfo
uzh.workflow.sourceCrossref:10.1002/rsa.21219
uzh.workflow.statusarchive
uzh.wos.impact1
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