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Polynomial Mixing of the Edge-Flip Markov Chain for Unbiased Dyadic Tilings *

unpublished

We give the first polynomial upper bound on the mixing time of the edge-flip Markov chain for unbiased dyadic tilings, resolving an open problem originally posed by Janson, Randall, and Spencer in 2002 [16]. A dyadic tiling of size n is a tiling of the unit square by n non-overlapping dyadic rectangles, each of area 1/n, where a dyadic rectangle is any rectangle that can be written in the form [a2 −s , (a + 1)2 −s ] × [b2 −t , (b + 1)2 −t ] for a, b, s, t ∈ Z ≥0. The edge-flip Markov chain

fatcat:dxiztbpuhnalpmi2hncxebdl44