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The centrality or the number of initial-state sources V of the system produced in heavy ion collision is a concept that is not uniquely defined and subject to significant theoretical and experimental uncertainties. We argue that a more robust connection between the initial-state sources with final-state multiplicity could be established from the event-by-event multiplicity correlation between two subevents separated in pseudorapidity, N_{a} vs N_{b}. This correlation is sensitive to two main types of centrality fluctuations (CF): (1) particle production for each source p(n) which smears the relation between V and N_{a} used for experimental centrality and (2) decorrelations between the sources in the two subevents V_{b} and V_{a}. The CF is analyzed in terms of cumulants of V_{b} and N_{b} as a function of N_{a}, i.e., experimental centrality is defined with N_{a}. We found that the mean values 〈V_{b}〉_{N_{a}} and 〈N_{b}〉_{N_{a}} increase linearly with N_{a} in midcentral collisions but flatten out in ultracentral collisions. Such nonlinear behavior is sensitive to the centrality resolution of N_{a}. In the presence of centrality decorrelations, the scaled variances 〈(δV_{b})^{2}〉/〈V_{b}〉 and 〈(δN_{b})^{2}〉/〈N_{b}〉 are found to decrease linearly with N_{a} in midcentral collisions, while the p(n) leads to another sharp decrease in the ultracentral region. The higher-order cumulants of V_{b} and N_{b} show interesting but rather complex behaviors which deserve further studies. Our results suggest that one can use the cumulants of the two-dimensional multiplicity correlation, especially the mean and variance, to constrain the particle production mechanism as well as the longitudinal fluctuations of the initial-state sources.