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- Measurement of multi-particle azimuthal correlations in $pp$, $p+$Pb and low-multiplicity Pb$+$Pb collisions with the ATLAS detectorPublication . ATLAS collaboration (2841 authors); Aguilar-Saavedra, Juan Antonio; Amor Dos Santos, Susana Patricia; Anjos, Nuno; Araque, Juan Pedro; Carvalho, João; Castro, Nuno Filipe; Conde Muiño, Patricia; Da Cunha Sargedas De Sousa, Mario Jose; Fiolhais, Miguel; Galhardo, Bruno; Gomes, Agostinho; Gonçalo, Ricardo; Jorge, Pedro; Machado Miguens, Joana; Maio, Amélia; Maneira, José; Oleiro Seabra, Luis Filipe; Onofre, António; Pedro, Rute; Santos, Helena; Saraiva, João; Silva, José; Tavares Delgado, Ademar; Veloso, Filipe; Wolters, HelmutMulti-particle cumulants and corresponding Fourier harmonics are measured for azimuthal angle distributions of charged particles in $pp$ collisions at $\sqrt{s}$ = 5.02 and 13 TeV and in $p$ + Pb collisions at $\sqrt{s_{_\text {NN}}}$ = 5.02 TeV, and compared to the results obtained for low-multiplicity $\mathrm{Pb}~+~\mathrm{Pb}$ collisions at $\sqrt{s_{_\text {NN}}}$ = 2.76 TeV. These measurements aim to assess the collective nature of particle production. The measurements of multi-particle cumulants confirm the evidence for collective phenomena in $p$ + Pb and low-multiplicity $\mathrm{Pb}~+~\mathrm{Pb}$ collisions. On the other hand, the $pp$ results for four-particle cumulants do not demonstrate collective behaviour, indicating that they may be biased by contributions from non-flow correlations. A comparison of multi-particle cumulants and derived Fourier harmonics across different collision systems is presented as a function of the charged-particle multiplicity. For a given multiplicity, the measured Fourier harmonics are largest in $\mathrm{Pb}~+~\mathrm{Pb}$ , smaller in $p$ + Pb and smallest in $pp$ collisions. The $pp$ results show no dependence on the collision energy, nor on the multiplicity.