  Volume or centrality fluctuations (CF) is one of the main uncertainties for
interpreting the centrality dependence of many experimental observables. The CF
is constrained by centrality selection based on particle multiplicity in a
reference subevent, and contributes to observables measured in another
subevent. Using a Glauber-based independent source model, we study the
influence of CF on several distributions of multiplicity $N$ and eccentricities
$\epsilon_n$: $p(N)$, $p(\epsilon_n)$, $p(\epsilon_n,\epsilon_m)$ and
$p(N,\epsilon_n)$, where the effects of CF is quantified using multi-particle
cumulants of these distributions. In mid-central collisions, a general relation
is established between the multiplicity fluctuation and resulting CF in the
reference subevent. In ultra-central collisions, where distribution of particle
production sources is strongly distorted, we find these cumulants exhibit rich
sign-change patterns, due to observable-dependent non-Gaussianity in the
underlying distributions. The details of sign-change pattern change with the
size of the collision systems. Simultaneous comparison of these different types
cumulants between model prediction and experimental data can be used to
constrain the CF and particle production mechanism in heavy-ion collisions.
Since the concept of centrality and CF are expected to fluctuate in the
longitudinal direction within a single event, we propose to use
pseudorapidity-separated subevent cumulant method to explore the nature of
intra-event fluctuations of centrality and collective dynamics. The subevent
method can be applied for any bulk observable that is sensitive to centrality,
and has the potential to separate different mechanisms for multiplicity and
flow fluctuations happening at different time scales. The forward detector
upgrades at RHIC and LHC will greatly enhance such studies in the future.
