作者：Haas, Benedicte; Miermont, Gregory; Pitman, Jim; Winkel, Matthias
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Paris Saclay; University of California System; University of California Berkeley; University of Oxford
摘要：Given any regularly varying dislocation we measure, We identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous's beta-splitting models and Ford's alpha models for phylogenetic trees. limits of Aldous's beta-splitting, models and Ford's alpha models for phylogenetic trees. This confirms in a strong way that the whole trees row at the same speed as the mean heig...
作者：Barany, Imre; Vu, Van
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London; Rutgers University System; Rutgers University New Brunswick
作者：van den Berg, J.
摘要：One of the most well-known classical results for site percolation on the square lattice is the equation p(c) + p(c)* = 1. In words, this equation means that for all vaues not equal p(c) of the Parameter p. the following holds: either a.s. there is all infinite open cluster or a.s. there is an infinite closed star cluster. This result is closely related to the percolation transition being sharp: below p(c), the size of the open cluster of a given vertex is not only (a.s.) finite. but has a dist...
