Cutoff for Contingency Table and Torus Random Walks with Low Incremental Correlations

Abstract We use the correlation matrix of the generating distribution to determine the mixing time for random walks on the torus $$(\mathbb {Z}/q\mathbb {Z})^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Z</mml:mi> <mml:mo>/</mml:mo> <mml:mi>q</mml:mi> <mml:mi>Z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> . We present our method in the context of the Diaconis–Gangolli random walk on both the $