  Initial partonic eccentricities in Au+Au collisions at center-of-mass energy
$\sqrt{s_{NN}}$ = 200 GeV are investigated using a multi-phase transport model
with string melting scenario. The initial eccentricities in different order of
harmonics are studied using participant and cumulant definitions. Eccentricity
in terms of second-, fourth- and sixth order cumulants as a function of number
of participant nucleons are compared systematically with the traditional
participant definition. The ratio of the cumulant eccentricities
$\varepsilon\left\{4\right\}/\varepsilon\left\{2\right\}$ and
$\varepsilon\left\{6\right\}/\varepsilon\left\{4\right\}$ are studied in
comparison with the ratio of the corresponding flow harmonics. The conversion
coefficients ($v_n/\varepsilon_n$) are explored up to fourth order harmonic
based on cumulant method. Furthermore, studies on transverse momentum ($p_T$)
and pseudo-rapidity ($\eta$) dependencies of eccentricities and their
fluctuations are presented. As in ideal hydrodynamics initial eccentricities
are expected to be closely related to the final flow harmonics in relativistic
heavy-ion collisions, studies of the fluctuating initial condition in the AMPT
model will shed light on the tomography properties of the initial source
geometry.
