  This article addresses an equidistribution problem concerning the zeros of
systems of random holomorphic sections of positive line bundles on compact
K\"{a}hler manifolds and random polynomials on $\mathbb{C}^{m}$ in the setting
of a compact subset. For random polynomials, we consider non-orthonormal bases
and prove an equidistribution result which is more general than the ones
acquired before for non-discrete probability measures. More precisely, our
result demonstrates that the equidistribution holds true even when the random
coefficients in the basis representation are not independentand identically
distributed (i.i.d.), and moreover, they are not constrained to any particular
probability distribution function. For random holomorphic sections, by
extending the concept of a sequence of asymptotically Bernstein-Markov measures
introduced by Levenberg, Bloom and Bayraktar in their recent paper to the
setting of holomorphic line bundles over compact Kahler manifolds, we derive a
global equidistribution theorem related to the zeros of systems of random
holomorphic sections for large tensor powers of a fixed holomorphic line bundle
for any codimension k, generalizing a previous result of Bayraktar in his 2016
paper and giving a positive answer to a question posed in the same paper. In
both settings using the variance estimation technique in another study of the
author with Bojnik plays an important role.
