The distribution of the number of clusters in the Arratia flow
Анотація
In this paper we study the distribution of the number of elements in the image of a closed interval under the action of the Arratia flow. We present two possible approaches to finding this distribution. The first is based on the well-known Karlin-McGregor formula and the second on the Pfaffian formulae for systems of coalescing and annihilating Brownian motions recently obtained in We also show that the corresponding mean value can be found using the notion of the total free time of particles in the Arratia flow introduced in [3].
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