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A new method is presented for determining event-by-event fluctuations ofelliptic flow, $v_2$, using first-order event planes. By studying theevent-by-event distributions of $v_2$ observables and first-order event-planeobservables, average flow $\avg{v_2}$ and event-by-event flow fluctuations canbe separately determined, making appropriate allowance for the effects offinite multiplicity and non-flow. The method has been tested with Monte Carlosimulations. The connection between flow fluctuations and fluctuations of theinitial-state participant eccentricity is discussed.Comment: 5 pages, 2 figures. Submitted to Phys. Rev. C. The discussions about  the assumptions in this paper have been added, as required by the refere

Method for determining event-by-event elliptic flow fluctuations based on the first-order event plane in heavy-ion collisions