A Signed Generalization of the Bernoulli–Laplace Diffusion Model

Clyde H. Schoolfield ()
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Clyde H. Schoolfield: Harvard University

Journal of Theoretical Probability, 2002, vol. 15, issue 1, 97-127

Abstract: 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 ( $${\mathbb{Z}}$$ 2≀S n )/(S r ×S n−r ). Specifically, for r not too far from n/2, we determine that, to first order in n, $$\tfrac{1}{4}$$ 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: Bernouilli–Laplace diffusion; Markov chain; hyperoctahedral group; homogeneous space; Fourier transform (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1013841306577

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