Random walks on finite groups and application to statistics

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1. We studied random walks on finite groups by using representation theory of finite groups, especially evaluation of their convergency ratio.2. Applying the result of 1, we show that a random walk on a symmetric group induces a random sampling of covergency tables.3. Applying some methods of algebraic geometry, we studies a problem in metal archaeology (lead isotope method with mixture of leads). 2 and 3 look unrelated, but Markokv spaces (higher dimentional simplexes) appear in both fields.4. We studied Burnside rings and Mackey functors on Markov spaces in representation theory.