<div class="csl-bib-body">
<div class="csl-entry">Banderier, C., Kuba, M., & Wallner, M. (2023, June 26). <i>Phase transitions of composition schemes: Mittag-Leffler and mixed Poisson distributions</i> [Conference Presentation]. The 34th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms 2023, Taipei, Taiwan (Province of China). http://hdl.handle.net/20.500.12708/191568</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191568
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dc.description.abstract
Multitudinous combinatorial structures are counted by generating functions satisfying a composition scheme F(z)=G(H(z)). The corresponding asymptotic analysis becomes challenging when this scheme is critical (i.e., G and~H are simultaneously singular). The singular exponents appearing in the Puiseux expansions of G and H then dictate the asymptotics. In this work, we first complement results of Flajolet et al. For a full family of singular exponents of G and~H. Motivated by many examples (random mappings, planar maps, directed lattice paths), we consider a natural extension of this scheme, namely F(z,u)=G(uH(z))M(z). We also consider a variant of this scheme, which allows us to analyse the number of H-components of a given size in~F. These two models lead to a rich world of limit laws, where we identify the key rôle played by a new universal three-parameter law: the beta-Mittag-Leffler distribution, which is essentially the product of a beta and a Mittag-Leffler distribution. We prove (double) phase transitions, additionally involving Boltzmann and mixed Poisson distributions, with a unified explanation of the associated thresholds. We also obtain moment convergence and local limit theorems. We end with extensions of the critical composition scheme to a cycle scheme and to the multivariate case, leading to product distributions. Applications are presented for random walks, trees (supertrees of trees, increasingly labelled trees, preferential attachment trees),triangular P\'olya urns, and the Chinese restaurant process. Joint work with Markus Kuba and Michael Wallner.
en
dc.language.iso
en
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dc.subject
Generating functions
en
dc.subject
Limit Laws
en
dc.subject
Mittag-Leffler distributions
en
dc.title
Phase transitions of composition schemes: Mittag-Leffler and mixed Poisson distributions
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
University of Applied Sciences Technikum Wien, Austria
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dc.type.category
Conference Presentation
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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tuw.author.orcid
0000-0003-0755-3022
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tuw.author.orcid
0000-0001-7188-6601
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tuw.author.orcid
0000-0001-8581-449X
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tuw.event.name
The 34th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms 2023
en
tuw.event.startdate
26-06-2023
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tuw.event.enddate
30-06-2023
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tuw.event.online
Hybrid
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tuw.event.type
Event for scientific audience
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tuw.event.place
Taipei
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tuw.event.country
TW
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tuw.event.institution
Academia Sinica
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tuw.event.presenter
Wallner, Michael
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tuw.event.track
Single Track
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.openairetype
conference paper not in proceedings
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item.fulltext
no Fulltext
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item.grantfulltext
none
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item.languageiso639-1
en
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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item.cerifentitytype
Publications
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
