A probabilistic computation of a Mehta integral
Liviu I. Nicolaescu
TL;DR
This paper employs the Kac-Rice formula to analytically compute the Mehta integral, which is crucial for understanding the normalization in Gaussian Orthogonal Ensemble statistics.
Contribution
It introduces a novel probabilistic approach using the Kac-Rice formula to evaluate the Mehta integral for the GOE.
Findings
Derived an explicit expression for the Mehta integral
Provided a new probabilistic proof of the integral's value
Enhanced understanding of normalization constants in random matrix theory
Abstract
We use the Kac-Rice formula to compute the Mehta integral describing the normalization constant arising in the statistics of the Gaussian Orthogonal Ensemble.
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Taxonomy
TopicsAdvanced Statistical Methods and Models · Multidisciplinary Science and Engineering Research · Simulation Techniques and Applications