A class of Markov chains with no spectral gap (Q2855909)
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scientific article; zbMATH DE number 6218159
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A class of Markov chains with no spectral gap |
scientific article; zbMATH DE number 6218159 |
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A class of Markov chains with no spectral gap (English)
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23 October 2013
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orthogonal polynomials
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Markov chains
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The authors, using \textit{T. Koornwinder}'s method from [Can. Math. Bull. 27, 205--214 (1984; Zbl 0507.33005)], construct positive recurrent Markov chains from the Jacobi orthogonal polynomials. A spectral measure for this Markov chain contains a point mass at \(x=1\). Then they derive an asymptotic upper bound on the total variation distance in the stationary distribution for \(a>-1\) and \(b>-1\). For the case of Chebyshev type polynomials (\(a=b=-1/2\)) they produce both asymptotic lower and upper bounds for the total variation distance. They also compare their results with related ones using other techniques.
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