@article{6167d7952e124e289194dab9d04cba28, title = "Two-dimensional volume-frozen percolation: Exceptional scales", abstract = "We study a percolation model on the square lattice, where clusters {"}freeze{"} (stop growing) as soon as their volume (i.e., the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when they reach diameter at least N was studied in van den Berg, de Lima and Nolin [Random Structures Algorithms 40 (2012) 220-226] and Kiss [Probab. Theory Related Fields 163 (2015) 713-768]. Using volume as a way to measure the size of a cluster - instead of diameter - leads, for large N, to a quite different behavior (contrary to what happens on the binary tree van den Berg, Kiss and Nolin [Electron. Commun. Probab. 17 (2012) 1-11], where the volume model and the diameter model are {"}asymptotically the same{"}). In particular, we show the existence of a sequence of {"}exceptional{"} length scales.", keywords = "Frozen percolation, Near-critical percolation, Sol-gel transitions", author = "{VAN DEN BERG}, Jacob and Pierre NOLIN", year = "2017", month = feb, doi = "10.1214/16-AAP1198", language = "English", volume = "27", pages = "91--108", journal = "Annals of Applied Probability", issn = "1050-5164", publisher = "Institute of Mathematical Statistics", number = "1", }