Double coset Markov chains

Abstract Let G be a finite group. $H, K$ subgroups of and $H \backslash / the double coset space. If Q is probability on which constant conjugacy classes ( $Q(s^{-1} t s) = Q(t)$ ), then random walk driven by projects to Markov chain /K$ . This allows analysis lumped using representation theory Examples include coagulation-fragmentation processes natural chains contingency tables. Our main example transvections $GL_n(q)$ onto $S_n$ via Bruhat decomposition. The has Mallows stationary distribution interesting mixing time behavior. projection illuminates combinatorics Gaussian elimination. Along way, we give sum in Hecke algebra cosets, describes as mixture Metropolis chains. Some extensions examples with compact group are discussed.