{"id":357389,"date":"2017-01-25T10:16:37","date_gmt":"2017-01-25T18:16:37","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/?post_type=msr-research-item&p=357389"},"modified":"2018-10-16T19:59:15","modified_gmt":"2018-10-17T02:59:15","slug":"mixing-upper-triangular-matrix-walk","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/mixing-upper-triangular-matrix-walk\/","title":{"rendered":"Mixing Of The Upper Triangular Matrix Walk"},"content":{"rendered":"

We study a natural random walk over the upper triangular matrices, with entries in the field $\\Z_2$<\/span><\/span><\/span>, generated by steps which add row i<\/span>+<\/span>1<\/span><\/span><\/span><\/span> to row i<\/span><\/span><\/span><\/span>. We show that the mixing time of the lazy random walk is O<\/span>(<\/span>n<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span> 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 $\\Z_q$<\/span><\/span><\/span> for q<\/span><\/span><\/span><\/span> prime.<\/p>\n","protected":false},"excerpt":{"rendered":"

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(n2) which is optimal up to constants. 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