A Signed Generalization of the Bernoulli–Laplace Diffusion Model

We bound the rate of convergence to stationarity for a signed generalization of the Bernoulli–Laplace diffusion model; this signed generalization is a Markov chain on the homogeneous space ( Z2(wreath product)S n )/(S r *S n–r ). Specifically, for r not too far from n/2, we determine that, to first order in n, n log n steps are both necessary and sufficient for total variation distance to become small. Moreover, for r not too far from n/2, we show that our signed generalization also exhibits the “cutoff phenomenon.”