Multi-particle azimuthal correlations for extracting event-by-event elliptic and triangular flow in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV

We present measurements of elliptic and triangular azimuthal anisotropy of charged particles detected at forward rapidity $1u003c|eta|u003c3$ in Au$+$Au collisions at $sqrt{s_{_{NN}}}=200$ GeV, as a function of centrality. The multiparticle cumulant technique is used to obtain the elliptic flow coefficients $v_2{2}$, $v_2{4}$, $v_2{6}$, and $v_2{8}$, and triangular flow coefficients $v_3{2}$ and $v_3{4}$. Using the small-variance limit, we estimate the mean and variance of the event-by-event $v_2$ distribution from $v_2{2}$ and $v_2{4}$. In a complementary analysis, we also use a folding procedure to study the distributions of $v_2$ and $v_3$ directly, extracting both the mean and variance. Implications for initial geometrical fluctuations and their translation into the final state momentum distributions are discussed.