  The Random Sequential Adsorption (RSA) problem holds crucial theoretical and
practical significance, serving as a pivotal framework for understanding and
optimizing particle packing in various scientific and technological
applications. Here the problem of the one-dimensional RSA of k-mers onto a
substrate with correlated defects controlled by uniform and power-law
distributions is theoretically investigated: the coverage fraction is obtained
as a function of the density of defects and several scaling laws are examined.
The results are compared with extensive Monte Carlo simulations and more
traditional methods based on master equations. Emphasis is given in elucidating
the scaling behavior of the fluctuations of the coverage fraction. The
phenomenon of universality breaking and the issues of conventional gaussian
fluctuations and the L\'evy type fluctuations from a simple perspective,
relying on the Central Limit Theorem, are also addressed.
