The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles

DOI10.1214/12-AIHP484zbMath1284.60171arXiv1105.2315MaRDI QIDQ376684

Ashkan Nikeghbali, Dirk Zeindler

Publication date: 19 November 2013

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.2315

zbMATH Keywords

symmetric groupPoisson approximationcycle countsmod-Poisson convergencetotal number cyclesweighted probability measure

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Combinatorial probability (60C05) Power series (including lacunary series) in one complex variable (30B10) Large deviations (60F10) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (8)

Mod-\(\phi\) convergence: approximation of discrete measures and harmonic analysis on the torus ⋮ Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves ⋮ Mod-\( \phi\) convergence of Stirling distributions and limit theorems for zeros of their generating functions ⋮ Limit distributions for Euclidean random permutations ⋮ Random permutation matrices under the generalized Ewens measure ⋮ Random permutations with logarithmic cycle weights ⋮ Asymptotic statistics of cycles in surrogate-spatial permutations ⋮ Cycle length distributions in random permutations with diverging cycle weights

Cites Work

• Unnamed Item
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• Random permutations with cycle weights
• Spatial random permutations and Poisson-Dirichlet law of cycle lengths
• Mellin transforms and asymptotics: Harmonic sums
• Spatial random permutations with small cycle weights
• The population structure associated with the Ewens sampling formula
• Singularity analysis and asymptotics of Bernoulli sums
• Logarithmic combinatorial structures: A probabilistic approach
• Asymptotic expansions for the Stirling numbers of the first kind
• Lindelöf representations and (non-)holonomic sequences
• Mod-discrete expansions
• Spatial random permutations and infinite cycles
• The sampling theory of selectively neutral alleles
• Cycle structure of random permutations with cycle weights
• Mod-Gaussian convergence: new limit theorems in probability and number theory
• Mod-Poisson Convergence in Probability and Number Theory
• Singularity Analysis of Generating Functions
• Limit Measures Arising in the Asympyotic Theory of Symmetric Groups. I.
• Asymptotics of poisson approximation to random discrete distributions: an analytic approach
• Ordered Cycle Lengths in a Random Permutation

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