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arXiv · 1603.04537

A pathwise interpretation of the Gorin-Shkolnikov identity

Yuu Hariya
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Abstract

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 note, 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. 2016-03-15. A pathwise interpretation of the Gorin-Shkolnikov identity. https://doi.org/10.1214/16-ecp10

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