Open Access
2016 A pathwise interpretation of the Gorin-Shkolnikov identity
Yuu Hariya
Electron. Commun. Probab. 21: 1-6 (2016). DOI: 10.1214/16-ECP10


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.


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Yuu Hariya. "A pathwise interpretation of the Gorin-Shkolnikov identity." Electron. Commun. Probab. 21 1 - 6, 2016.


Received: 22 March 2016; Accepted: 18 July 2016; Published: 2016
First available in Project Euclid: 26 July 2016

zbMATH: 1346.60130
MathSciNet: MR3533284
Digital Object Identifier: 10.1214/16-ECP10

Primary: 60J55 , 60J65

Keywords: Jeulin’s identity , Local time , Normalized Brownian excursion

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