Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Displacement convexity for the generalized orthogonal ensemble.
AU - Blower, Gordon
N1 - The original publication is available at www.springerlink.com
PY - 2004/9
Y1 - 2004/9
N2 - 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.
AB - 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.
KW - random matrices
KW - statistical mechanics
U2 - 10.1023/B:JOSS.0000041742.86859.cd
DO - 10.1023/B:JOSS.0000041742.86859.cd
M3 - Journal article
VL - 116
SP - 1359
EP - 1387
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 5/6
ER -