%0 Generic %1 gnedin2011lambdacoalescents %A Gnedin, Alexander %A Iksanov, Alexander %A Marynych, Alexander %D 2011 %K lambda_coalescent %T Lambda-coalescents with dust component %U http://arxiv.org/abs/1102.1146 %X We consider the lambda-coalescent processes with positive frequency of singleton clusters. The class in focus covers, for instance, the beta$(a,b)$-coalescents with $a>1$. We show that some large-sample properties of these processes can be derived by coupling the coalescent with an increasing Lévy process (subordinator), and by exploiting parallels with the theory of regenerative composition structures. In particular, we discuss the limit distributions of the absorption time and the number of collisions.

@misc{gnedin2011lambdacoalescents, abstract = { We consider the lambda-coalescent processes with positive frequency of singleton clusters. The class in focus covers, for instance, the beta$(a,b)$-coalescents with $a>1$. We show that some large-sample properties of these processes can be derived by coupling the coalescent with an increasing L{\'e}vy process (subordinator), and by exploiting parallels with the theory of regenerative composition structures. In particular, we discuss the limit distributions of the absorption time and the number of collisions. }, added-at = {2011-02-21T07:41:44.000+0100}, author = {Gnedin, Alexander and Iksanov, Alexander and Marynych, Alexander}, biburl = {https://www.bibsonomy.org/bibtex/295c1c146723c479c2138e560b10b4528/peter.ralph}, description = {[1102.1146] Lambda-coalescents with dust component}, interhash = {463d2229415d4b4dcd57b783e37ac183}, intrahash = {95c1c146723c479c2138e560b10b4528}, keywords = {lambda_coalescent}, note = {cite arxiv:1102.1146 Comment: 21 pages}, timestamp = {2011-02-21T07:41:44.000+0100}, title = {Lambda-coalescents with dust component}, url = {http://arxiv.org/abs/1102.1146}, year = 2011 }