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The law of the iterated logarithm for character ratios

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  • Su, Zhonggen

Abstract

Recently, Fulman developed some general connections between martingales and character ratios of a random representation of the symmetric group on transitions, and obtained a convergence rate in a central limit theorem. In this work we aim to establish the law of the iterated logarithm for character ratios. The technique is a well-known Skorokhod embedding theorem for martingales and strong approximation argument. Also, bounded martingale difference methods are used to obtain a large deviation for character ratios.

Suggested Citation

  • Su, Zhonggen, 2005. "The law of the iterated logarithm for character ratios," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 337-346, March.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:337-346
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    References listed on IDEAS

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    1. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
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