# On the size of the block of 1 for $\varXi$-coalescents with dust

@inproceedings{Freund2017OnTS, title={On the size of the block of 1 for \$\varXi\$-coalescents with dust}, author={Fabian Freund and Martin Mohle}, year={2017} }

We study the frequency process $f_1$ of the block of 1 for a $\varXi$-coalescent $\varPi$ with dust. If $\varPi$ stays infinite, $f_1$ is a jump-hold process which can be expressed as a sum of broken parts from a stick-breaking procedure with uncorrelated, but in general non-independent, stick lengths with common mean. For Dirac-$\varLambda$-coalescents with $\varLambda=\delta_p$, $p\in[\frac{1}{2},1)$, $f_1$ is not Markovian, whereas its jump chain is Markovian. For simple $\varLambda…

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