Phase transitions of composition schemes: Mittag-Leffler and mixed Poisson distributions

DOI10.1214/24-aap2076MaRDI QIDQ6620079

Cyril Banderier, Michael Wallner, Markus Kuba

Publication date: 16 October 2024

Published in: The Annals of Applied Probability (Search for Journal in Brave)

generating functions stable laws singularity analysis analytic combinatorics Mittag-Leffler distributions Boltzmann distributions mixed Poisson distributions critical composition schemes

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Sums of independent random variables; random walks (60G50) Exact enumeration problems, generating functions (05A15) Combinatorial probability (60C05)

Cites Work

Fluctuation Theory of Recurrent Events
The representation of 𝑒^{-𝑥^{𝜆}} as a Laplace integral
On bucket increasing trees, clustered increasing trees and increasing diamonds
Sur les équations intégrales singulières à noyau réel et symétrique.
Exact-Size Sampling of Enriched Trees in Linear Time
Stable graphs: distributions and line-breaking construction
Gibbs partitions: a comprehensive phase diagram
Local time for lattice paths and the associated limit laws
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
On moment sequences and mixed Poisson distributions
Addendum to ``Moments of gamma type and the Brownian supremum process area
Combinatorial families of multilabelled increasing trees and hook-length formulas
A proof of the generalized second limittheorem in the theory of probability.
Gaussian limiting distributions for the number of components in combinatorial structures
Generalized Stirling permutations, families of increasing trees and urn models
Bilabelled increasing trees and hook-length formulae
Marking in combinatorial constructions: Generating functions and limiting distributions
General combinatorial schemas: Gaussian limit distributions and exponential tails
Martingale functional central limit theorems for a generalized Pólya urn
Generalized gamma approximation with rates for urns, walks and trees
On Mittag-Leffler functions and related distributions
Periodic Pólya urns, the density method and asymptotics of Young tableaux
École d'été de probabilités de Saint-Flour XIII - 1983
Descendants in increasing trees
Uniform recursive trees: branching structure and simple random downward walk
Profiles of random trees: Limit theorems for random recursive trees and binary search trees
Limit theorems for triangular urn schemes
On the degree distribution of the nodes in increasing trees
A combinatorial approach to the analysis of bucket recursive trees
Lamperti-type laws
On the uniform convergence of normalized Poisson mixtures to their mixing distribution
The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
Largest component in random combinatorial structures
Second phase changes in random \(m\)-ary search trees and generalized quicksort: Convergence rates
Logarithmic combinatorial structures: A probabilistic approach
Über den Fundamentalsatz in der Theorie der Funktionen \(E_\alpha(x)\).
Une généralisation de l'intégrale de \textit{Laplace-Abel}.
Sur la nouvelle fonction \(E_\alpha(x)\).
Basic analytic combinatorics of directed lattice paths
Lattice paths with catastrophes
Moment convergence of balanced Pólya processes
Enumeration and asymptotics of restricted compositions having the same number of parts
Boltzmann samplers for first-order differential specifications
Singularity analysis, Hadamard products, and tree recurrences
Analytic urns
The contraction method for recursive algorithms
Exchangeable and partially exchangeable random partitions
Some canonical sequences of integers
Limiting distributions for the number of inversions in labelled tree families
Degree asymptotics with rates for preferential attachment random graphs
A half-normal distribution scheme for generating functions
A Berry-Esseen theorem for Pitman's \(\alpha\)-diversity
The Prabhakar or three parameter Mittag-Leffler function: theory and application
The kernel method for lattice paths below a line of rational slope
Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
A line-breaking construction of the stable trees
Central and local limit theorems applied to asymptotic enumeration
Functional limit theorems for multitype branching processes and generalized Pólya urns.
On a new class of ``contagious distributions, applicable in entomology and bacteriology.
Growing random uniform \(d\)-ary trees
Random maps, coalescing saddles, singularity analysis, and Airy phenomena
Increasing Diamonds
Graph classes with given 3-connected components: Asymptotic enumeration and random graphs
Analytic Combinatorics in Several Variables
Limiting Distributions for a Class Of Diminishing Urn Models
Limit Theorems for Subtree Size Profiles of Increasing Trees
On death processes and urn models
Analysis of three graph parameters for random trees
Asymptotic enumeration and limit laws of planar graphs
Analysis of Statistics for Generalized Stirling Permutations
On Occupation Times for Markoff Processes
On the Unimodality of Geometric Stable Laws
Random cutting and records in deterministic and random trees
Limit laws for embedded trees: Applications to the integrated superBrownian excursion
Cutting down very simple trees
Singularity Analysis of Generating Functions
Polya Urn Models
Random Trees
Subtree Sizes in Recursive Trees and Binary Search Trees: Berry–Esseen Bounds and Poisson Approximations
Images and Preimages in Random Mappings
A probabilistic approach to block sizes in random maps
The Havriliak–Negami relaxation and its relatives: the response, relaxation and probability density functions
Asymptotic degree distribution in random recursive trees
Boltzmann Samplers for the Random Generation of Combinatorial Structures
The Maximum Degree of the Barabási–Albert Random Tree
On martingale tail sums in affine two-color urn models with multiple drawings
On the structure of random plane‐oriented recursive trees and their branches
Asymptotics of poisson approximation to random discrete distributions: an analytic approach
Chance and Stability
A restaurant process with cocktail bar and relations to the three-parameter Mittag–Leffler distribution
On complete monotonicity of three parameter Mittag-Leffler function
Uniform Asymptotics of Poisson Approximation to the Poisson-Binomial Distribution
The birth of the giant component
Neyman type A distribution revisited
Formulae and Asymptotics for Coefficients of Algebraic Functions
Level of nodes in increasing trees revisited
Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques
EM Algorithm for Mixed Poisson and Other Discrete Distributions
Mittag-Leffler Functions, Related Topics and Applications
Ancestors and descendants in evolving k‐tree models
Cutting down random trees