Geodesic
On extremal points of the space of symmetric stochastic matrices
Sbornik. Mathematics, Tome 25 (1975) no. 3, pp. 419-428

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Let $\Delta_n$ be the set of extremal points of the convex space of symmetric stochastic matrices of order $n$. Asymptotic formulas as $n\to\infty$ are found for the number of elements in $\Delta_n$, and limit distributions are given for the number of positive elements in a random probability matrix $C\in\Delta_n$ and for the characteristic multiplicity of a random mapping from a set of permutations in $\Delta_n$. Bibliography: 4 titles. 
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     author = {V. N. Sachkov},
     title = {On extremal points of the space of symmetric stochastic matrices},
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     number = {3},
     year = {1975},
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V. N. Sachkov. On extremal points of the space of symmetric stochastic matrices. Sbornik. Mathematics, Tome 25 (1975) no. 3, pp. 419-428. http://geodesic.mathdoc.fr/item/SM_1975_25_3_a4/