The Louis Vuitton Foundation Museum by Frank Gehry

The Louis Vuitton Foundation's museum near the Bois de Boulogne in Paris. Designed by Frank Gehry, it opens on Oct. 27.

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The center, on Paris’s western edge, is one of several private museums for contemporary art opening around the world in coming months at the behest of wealthy private patrons. Among them are Renzo Piano’s Centro Botín in Santander, Spain, commissioned by the banking magnate Emilio Botín, who died last month, and a museum planned by the financier and philanthropist Eli Broad in Los Angeles that is designed by Diller Scofidio & Renfro.

“Maybe now states are less powerful than before,” Jean-Paul Claverie, an adviser to Mr. Arnault, said of the trend. “And all the entrepreneurs are conscious of their place in society and have the means to realize it.”