DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 113-122

J. T. Chayes

Title: Finite-Size Scaling in Percolation

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\"os and R\'enyi.

1991 Mathematics Subject Classification: 82B43, 82B26, 60K35, 05C80

Keywords and Phrases: percolation, phase transitions, finite-size scaling

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