Blower, Gordon (2004) Displacement convexity for the generalized orthogonal ensemble. Journal of Statistical Physics, 116 (5/6). pp. 1359-1387. ISSN 0022-4715
The paper considers the generalized ensemble of n by n real symmetric matrices that is invariant under the natural action of the real orthogonal group and that is given by a real potential function. Under various conditions on the potential, the empirical eigenvalue distributions converge weakly almost surely to a non random equilibrium measure as n tends to infinity. The logarithmic energy is displacement convex as a functional on charge distributions with fixed mean on the real line for such potentials.
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