Feller property of the multiplicative coalescent with linear deletion

2016/09/30 by Rath, Balazs
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1610.00021

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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