A pathwise interpretation of the Gorin-Shkolnikov identity

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In a recent paper by Gorin and Shkolnikov (2016), they have found, as a corollary to their result relevant to random matrix theory, that the area below a normalized Brownian excursion minus one half of the integral of the square of its total local time, is identical in law with a centered Gaussian random variable with variance 1=12. In this paper, we give a pathwise interpretation to their identity; Jeulin’s identity connecting normalized Brownian excursion and its local time plays an essential role in the exposition.

Original languageEnglish
Article number52
JournalElectronic Communications in Probability
Publication statusPublished - 2016


  • Jeulin’s identity
  • Local time
  • Normalized Brownian excursion


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