Geodesic
Exact Expectation and Variance of Minimal Basis of Random Matroids
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 277-288

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We formulate and prove a formula to compute the expected value of the minimal random basis of an arbitrary finite matroid whose elements are assigned weights which are independent and uniformly distributed on the interval [0, 1]. This method yields an exact formula in terms of the Tutte polynomial. We give a simple formula to find the minimal random basis of the projective geometry PG(r − 1, q).
Keywords: minimal basis, q-analog, finite projective geometry, Tutte polynomial 
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     title = {Exact {Expectation} and {Variance} of {Minimal} {Basis} of {Random} {Matroids}},
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Kordecki, Wojciech; Łyczkowska-Hanćkowiak, Anna. Exact Expectation and Variance of Minimal Basis of Random Matroids. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 277-288. http://geodesic.mathdoc.fr/item/DMGT_2013_33_2_a2/