Percolation since Saint-flour
نویسندگان
چکیده
There has been a great deal of interest and activity in percolation theory since the two Saint-Flour courses, [76, 111], of 1984 and 1996 reprinted in this new edition. We present here a summary of progress since the first publications of our lecture notes. The second edition of Percolation, [77], was published in 1999 as a fairly complete, contemporary account of ‘classical’ percolation (but with only limited coverage of first-passage percolation). Books published since in the general area include [78, 79] and, for two-dimensional theory, [27]. There has been in addition a third Saint-Flour course on percolation, on the Wulff construction by Raphaël Cerf in 2004, [40]. The 2004 review by Howard of first-passage percolation, [103], is useful. The principal targets of this short introduction are to indicate areas of significance that have received attention in recent years, and to include a useful bibliography. It is not intended as a comprehensive survey of the vast amount of material related to percolation and published since 1984/1996. We restrict our attention mostly to problems associated with finite-dimensional lattices, and we take quite a broad view of what constitutes a percolation or firstpassage percolation problem. We offer apologies to the many authors whose work does not receive explicit mention here, and we trust sufficient pointers are present to guide the reader through recent developments in percolation theory.
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