English

A signed generalization of the Bernoulli-Laplace diffusion model

Probability 2012-08-27 v1

Abstract

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 (Z_2 \wr S_n) / (S_r \times S_{n-r}). Specifically, for r not too far from n/2, we determine that, to first order in n, 1/4 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.''

Keywords

Cite

@article{arxiv.math/0006119,
  title  = {A signed generalization of the Bernoulli-Laplace diffusion model},
  author = {Clyde H. Schoolfield,},
  journal= {arXiv preprint arXiv:math/0006119},
  year   = {2012}
}

Comments

39 pages. See also http://www.fas.harvard.edu/~chschool/ . Submitted for publication in May, 2000