Journal of Theoretical Probability

, Volume 32, Issue 2, pp 1051–1075 | Cite as

Asymptotic Expansion of Spherical Integral

  • Jiaoyang HuangEmail author


We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one. We prove the existence of the full asymptotic expansions of these spherical integrals and derive the first and the second term in the asymptotic expansion.


Random matrices Spherical integral Asymptotic expansion Free probability 

Mathematics Subject Classification (2010)

15B52 46L54 



This research was conducted at the Undergraduate Research Opportunities Program of the MIT Mathematics Department, under the direction of Prof. Alice Guionnet. I would like to express to her my warmest thanks both for introducing me to this problem and for her dedicated guidance throughout the research process. I want to also thank the anonymous reviewer for careful reading of the manuscript and helpful suggestions.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsHarvardCambridgeUSA

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