Abstract
We modify the definition of Aldous’ multiplicative coalescent process (Ann. Probab. 25 (1997) 812–854) 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 (J. Stat. Phys. 137 (2009) 459–499) and the so-called rigid representation of such scaling limits (Electron. J. Probab. To appear).
Citation
Balázs Ráth. "Feller property of the multiplicative coalescent with linear deletion." Bernoulli 25 (1) 221 - 240, February 2019. https://doi.org/10.3150/17-BEJ984
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