Mathematics Colloquia and Seminars

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Everybody knows that a matrix can be reduced to diagonal form using row operations (Gaussian elimination). If you work over a finite field, there are pivoting steps and these cost extra. In joint work with Mackenzie Simper and Arun Ram we study a dynamical version, following a random walk on $Gl(n,q)$ generated by random transvections. This in turn induces a Markov chain on permutations (with a 'Mallows' stationary distribution). There is a surprising speed up in rates of convergence (from $n$ to $\log n$) and some nice new math. It all generalizes (to general type) but this talk will be in probabilistic English.