{"id":152363,"date":"1998-06-01T00:00:00","date_gmt":"1998-06-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/finite-size-scaling-in-percolation\/"},"modified":"2018-10-16T19:56:13","modified_gmt":"2018-10-17T02:56:13","slug":"finite-size-scaling-in-percolation","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/finite-size-scaling-in-percolation\/","title":{"rendered":"Finite-Size Scaling in Percolation"},"content":{"rendered":"<div class=\"asset-content\">\n<p>This work is a detailed study of the phase transition in percolation, in particular of the question of finite-size scaling: Namely, how does the critical transition behavior emerge from the behavior of large, finite systems? Our results rigorously locate the proper window in which to do critical computation and establish features of the phase transition. This work is a finite-dimensional analogue of classic work on the critical regime of the random graph model of Erd\u00f6s and R\u00e9nyi.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This work is a detailed study of the phase transition in percolation, in particular of the question of finite-size scaling: Namely, how does the critical transition behavior emerge from the behavior of large, finite systems? Our results rigorously locate the proper window in which to do critical computation and establish features of the phase transition. 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