Feller property of the multiplicative coalescent with linear deletion

Ráth, Balázs (2016) Feller property of the multiplicative coalescent with linear deletion. Bernoulli Journal. ISSN 1350-7265, ESSN: 1573-9759 (In Press)

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Abstract

We modify the definition of Aldous' multiplicative coalescent process and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with a rate equal to the product of their sizes and clusters are deleted with a rate linearly proportional to their size. We prove that the MCLD is a Feller process. This result is a key ingredient in the description of scaling limits of the evolution of component sizes of the mean field frozen percolation model and the so-called rigid representation of such scaling limits.

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