Extended Void Merging Tree Algorithm for Self-Similar Models
  In hierarchical evolution, voids exhibit two different behaviors related with
their surroundings and environments, they can merge or collapse. These two
different types of void processes can be described by the two-barrier excursion
set formalism based on Brownian random walks. In this study, the analytical
approximate description of the growing void merging algorithm is extended by
taking into account the contributions of voids that are embedded into overdense
region(s) which are destined to vanish due to gravitational collapse. Following
this, to construct a realistic void merging model that consists of both
collapse and merging processes, the two-barrier excursion set formalism of the
void population is used. Assuming spherical voids in the Einstein de Sitter
Universe, the void merging algorithm which allows us to consider the two main
processes of void hierarchy in one formalism is constructed. In addition to
this, the merger rates, void survival probabilities, void size distributions in
terms of the collapse barrier and finally, the void merging tree algorithm in
the self-similar models are defined and derived.
