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SIXTY YEARS OF PERCOLATION

    https://doi.org/10.1142/9789813272880_0162Cited by:6 (Source: Crossref)
    Abstract:

    Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest in probability and mathematical physics. The golden age of percolation is probably the eighties, during which most of the major results were obtained for the most classical of these models, named Bernoulli percolation, but it is really the two following decades which put percolation theory at the crossroad of several domains of mathematics. In this broad review, we propose to describe briefly some recent progress as well as some famous challenges remaining in the field. This review is not intended to probabilists (and a fortiori not to specialists in percolation theory): the target audience is mathematicians of all kinds.

    This research was funded by an IDEX Chair from Paris Saclay, by the NCCR SwissMap from the Swiss NSF and the ERC grant 757296 CRIBLAM. We thank David Cimasoni, Sébastien Martineau, Aran Raoufi and Vincent Tassion for their comments on the manuscript.
    MSC2010: 82B43