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In hierarchical evolution, voids exhibit two different behaviors related withtheir surroundings and environments, they can merge or collapse. These twodifferent types of void processes can be described by the two-barrier excursionset formalism based on Brownian random walks. In this study, the analyticalapproximate description of the growing void merging algorithm is extended bytaking into account the contributions of voids that are embedded into overdenseregion(s) which are destined to vanish due to gravitational collapse. Followingthis, to construct a realistic void merging model that consists of bothcollapse and merging processes, the two-barrier excursion set formalism of thevoid population is used. Assuming spherical voids in the Einstein de SitterUniverse, the void merging algorithm which allows us to consider the two mainprocesses of void hierarchy in one formalism is constructed. In addition tothis, the merger rates, void survival probabilities, void size distributions interms of the collapse barrier and finally, the void merging tree algorithm inthe self-similar models are defined and derived.

Extended Void Merging Tree Algorithm for Self-Similar Models