Exponential Approximation by Stein’s Method and Spectral Graph Theory
نویسندگان
چکیده
General Berry-Esséen bounds are developed for the exponential distribution using Stein’s method and a new concentration inequality approach. As an application, a sharp error term is obtained for Hora’s result that the spectrum of the Johnson graph has an exponential limit.
منابع مشابه
Exponential Approximation by Stein’s Method and Spectral Graph Theory Running head: Exponential Approximation by Stein’s Method
Running head: Exponential Approximation by Stein’s Method Version of 8/16/08 By Sourav Chatterjee, Jason Fulman, and Adrian Röllin Abstract: General Berry-Esséen bounds are developed for the exponential distribution using Stein’s method. As an application, a sharp error term is obtained for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is t...
متن کاملExponential Approximation by Stein’s Method and Spectral Graph Theory Running head: Exponential Approximation by Stein’s Method Version of 8/16/08
General Berry-Esséen bounds are developed for the exponential distribution using Stein's method. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is the first use of Stein's method to study the spectrum of a graph with a non-normal limit.
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Running head: Exponential Approximation by Exchangeable Pairs Version of 4/7/06 By Sourav Chatterjee and Jason Fulman Abstract: A general Berry-Esseen bound is obtained for the exponential distribution using Stein’s method of exchangeable pairs. As an application, an error term is derived for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is...
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The purpose of this paper is to further develop exponential approximation, using Stein’s method of exchangeable pairs. The first use of exchangeable pairs in exponential approximation was in the paper Chatterjee et al. (2011), which studied the spectrum of the Bernoulli-Laplace Markov chain. Unfortunately the results in Chatterjee et al. (2011), which use the Kolmogorov metric, are very complic...
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