Mixing of the upper triangular matrix walk

Yuval Peres; Allan Sly

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arXiv · 1105.4402

Mixing of the upper triangular matrix walk

Yuval Peres·Allan Sly

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Abstract

We study a natural random walk over the upper triangular matrices, with entries in the field $\Z_2$, generated by steps which add row $i+1$ to row $i$. We show that the mixing time of the lazy random walk is $O(n^2)$ which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields $\Z_q$ for $q$ prime.

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Yuval Peres, Allan Sly. 2011-05-23. Mixing of the upper triangular matrix walk. https://arxiv.org/abs/1105.4402

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