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Michael Erlihson

Publications and source records attributed to Michael Erlihson.

3 recordsLinked to original sources
arXiv2007

Meinardus' theorem on weighted partitions: extensions and a probabilistic proof

We give a probalistic proof of the famous Meinardus' asymptotic formula for the number of weighted partitions with weakened one of the three Meinardus' conditions, and extend the resulting version of the theorem to other two classis types of decomposable combinatorial structures, which are called assemblies and selections. The results obtained are based on combining Meinardus' analytical approach with probabilistic method of Khitchine.

math.PR↗
arXiv2007

Limit shapes of multiplicative measures associated with coagulation-fragmentation processes and random combinatorial structures

We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, $a_k\sim Ck^{p-1}, k\to\infty, p>0$,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.

math.PR↗