On the number of collisions in beta2, b-coalescents
نویسنده
چکیده
Expansions are provided for the moments of the number of collisions Xn in the β(2, b)-coalescent restricted to the set {1, . . . , n}. We verify that Xn/EXn converges almost surely to one and that Xn, properly normalized, weakly converges to the standard normal law. These results complement previously known facts concerning the number of collisions in β(a, b)-coalescents with a ∈ (0,2) and b = 1, and a > 2 and b > 0. The case a = 2 is a kind of ‘border situation’ which seems not to be amenable to approaches used for a 6= 2.
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تاریخ انتشار 2009