<div class="csl-bib-body">
<div class="csl-entry">Wallner, M. (2022, February 3). <i>Phase transitions of composition schemes: Mittag-Leffler and mixed Poisson distributions</i> [Presentation]. Probability, Statistics and Combinatorics Seminar, Sweden. http://hdl.handle.net/20.500.12708/153003</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/153003
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dc.description.abstract
Multitudinous probabilistic and combinatorial objects are associated with generating functions satisfying a composition scheme F(z) = G(H(z)). The analysis becomes challenging when this scheme is critical (i.e., G and H are simultaneously singular). Motivated by many examples (random mappings, planar maps, directed lattice paths), we consider a natural extension of this scheme, namely F(z, u) = G(u H(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.
We prove that 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 also prove (double) phase transitions, additionally involving Boltzmann and mixed Poisson distributions. In all cases we obtain moment convergence and local limit theorems. We present several applications of our results for, e.g., random walks, trees, Pólya urns, and the Chinese restaurant process. Among other things, this allows us to answer a problem of Janson on the limit distribution of triangular Pólya urns
en
dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.subject
critical composition schemes
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dc.subject
Mixed Poisson distributions
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dc.subject
Mittag-Leffler distributions
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dc.subject
stable laws
en
dc.subject
Boltzmann distributions
en
dc.subject
Analytic Combinatorics
en
dc.subject
generating functions
en
dc.subject
singularity analysis
en
dc.title
Phase transitions of composition schemes: Mittag-Leffler and mixed Poisson distributions
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
P 34142-N
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dc.relation.grantno
J4162-N35
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dc.type.category
Presentation
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tuw.project.title
Gestreckte Exponenten und darüber hinaus
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tuw.project.title
Funktionsgleichungen für Gitter- und Baumstrukturen
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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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
0000-0001-8581-449X
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tuw.event.name
Probability, Statistics and Combinatorics Seminar
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tuw.event.startdate
03-03-2022
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tuw.event.enddate
03-03-2022
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tuw.event.online
Online
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tuw.event.type
Event for scientific audience
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tuw.event.country
SE
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tuw.event.presenter
Wallner, Michael
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tuw.presentation.online
Online
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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.languageiso639-1
en
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item.openairetype
conference presentation
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/R60J-J5BD
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
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crisitem.author.orcid
0000-0001-8581-449X
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crisitem.author.parentorg
E100 - Fakultät für Mathematik und Geoinformation
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crisitem.project.funder
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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crisitem.project.funder
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
