Geodesic
Angles of the Gaussian simplex
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 79-91

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Consider a $d$-dimensional simplex whose vertices are random points chosen independently according to the standard Gaussian distribution on $\mathbb R^d$. We prove that the expected angle sum of this random simplex equals the angle sum of the regular simplex of the same dimension $d$. 
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     author = {Z. Kabluchko and D. Zaporozhets},
     title = {Angles of the {Gaussian} simplex},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
     volume = {476},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_476_a4/}
}
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Z. Kabluchko; D. Zaporozhets. Angles of the Gaussian simplex. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 79-91. http://geodesic.mathdoc.fr/item/ZNSL_2018_476_a4/