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Bond Percolation on Isoradial Graphs

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We present the topic of percolation on planar graphs, focusing on the issue of universality. We give a universality result for the canonical percolation models on the so-called isoradial graphs. These are proved to be critical, to satisfy box-crossing (RSW) inequalities and to have universal arms exponents (assuming they exist). This is achieved by using the star-triangle transformation to obtain an equivalence extending over a set of bond percolation models on isoradial graphs. The work is joint with Geoffrey Grimmett.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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