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

@article{Cannon2017PolynomialMO, title={Polynomial Mixing of the Edge-Flip Markov Chain for Unbiased Dyadic Tilings}, author={S. Cannon and D. Levin and Alexandre Stauffer}, journal={ArXiv}, year={2017}, volume={abs/1611.03636} }

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. 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}] \times [b2^{-t}, (b+1)2^{-t}] for non-negative integers a,b,s,t. The edge-flip… CONTINUE READING

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