My First HK Probability Seminar
Yesterday, I attended my first Hong Kong Probability Seminar. Gefei Cai, from Peking, spoke about the 3 point connectivity problem in 2D critical percolation.
Perhaps I should heed Ravi Vakil’s advice and jot down three things that I had gained from the seminar.
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Apparently this is a very difficult problem. I had pondered about the n-point connectivity of a different and rather exotic (relatively trivial, from what I have seen so far) lattice. But I suppose this is a bit different since it is talking about the scaling limit and I was just considering a discrete case on a sort of degenerate lattice.
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It is quite amazing how much random geometry is in the study of critical statistical mechanical models. Before, I had sort of viewed random geometry as its own thing, where the main motivation is ‘What is a random surface?’. Obviously, I was influenced by Sheffield’s talk with the same name. Of course, I knew that it would basically be an SLE, CLE problem, but I had not expected the extent to which theories like LQG are applied. Well, I suppose I don’t really know what LQG is all about!
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I need to know more about random planar maps. They look like very discrete objects. Yet the only time I see them mentioned is along with LQG (mostly from Nina Holden), which seems to live in the continuum. And what the hell are circle packings?