2005/07/17 by Michael Erlihson, Erlihson, Michael, Boris L. Granovsky +2
Computer Science · Mathematics · #60J27 #82C22 #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR #msc:60J27 #msc:82C22
paper · pdf · doi:10.48550/arxiv.math/0507343
40 pages. The paper was extended and reorganized following referee's suggestions. It will be published in Ann. Inst. H. Poincare
openalex publication_date 2005/07/17 · arxiv created 2007/06/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼ Ckp-1, k→∞, p>0,where C is a positive constant. The measures considered are associated with reversible coagulation-fragmentation processes and certain combinatorial structures, known as assemblies. We prove the functional central limit theorem for the fluctuations of a scaled random partition from its limit shape. We demonstrate that when the component size passes beyond the threshold value, the independence of numbers of components transforms into their conditional independence. Among other things, the paper also discusses, in a general setting, the interplay between limit shapes, threshold and gelation.