A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is
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] × [b2^-t, (b+1)2^-t] for non-negative integers a,b,s,t. The edge-flip Markov chainarXiv:1611.03636v1 fatcat:gssfcjs5lrhadobw7tjngdlqwm