Equidistribution of zeros of random polynomials and random polynomial mappings in $\mathbb C^m$

We study an equidistribution problem for zeros of random polynomials represented with respect to a basis whose elements are so-called Z-asymptotically Chebyshev polynomials(which might not be orthonormal) in Cm. We use certain results obtained in a very recent work of Bayraktar, Bloom and Levenberg and have an equidistribution result in a more general probabilistic setting than what the paper of Bayraktar, Bloom and Levenberg considers even though the basis polynomials they use are more general than Z-asymptotically Chebyshev polynomials. Our equidistribution result is based on the expected distribution and the variance estimate of random zero currents associated with the zero sets of polynomials. This equidistribution result of general nature shows that equidistribution result turns out to be true without the random coefficients coming from the basis representation being i.i.d. (independent and identically distributed), which also means that there is no need to use any probability distribution function associated with these random coefficients. In the last section, making our assumptions on the random coefficients stronger, i.e. considering i.i.d. random variables whose probability distributions are previously very often studied and general enough (including Gaussian distributions), we have two different equidistribution results for codimensions bigger than 1 by looking into, first, the regular compact sets and bases of Z-asymptotically Chebyshev polynomials and later the orthogonal polynomials with respect to the L2-inner product defined by the weighted asymptotically Bernstein-Markov measures on a given locally regular compact set.