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The fluctuations of the jamming coverage upon Random Sequential Adsorption(RSA) are studied using both analytical and numerical techniques. Our mainresult shows that these fluctuations (characterized by $\sigma_{\theta_J}$)decay with the lattice size according to the power-law $\sigma_{\theta_J}\propto L^{-1/ \nu}$. The exponent $\nu$ depends on the dimensionality $D$ ofthe substrate and the fractal dimension of the set where the RSA processactually takes place ($d_f$) according to $\nu = 2 / (2D - d_f)$.Thistheoretical result is confirmed by means of extensive numerical simulationsapplied to the RSA of dimers on homogeneous and stochastic fractal substrates.Furthermore, our predictions are in excellent agreement with different previousnumerical results.  It is also shown that, studying correlated stochastic processes, one candefine various fluctuating quantities designed to capture either the underlyingphysics of individual processes or that of the whole system. So, subtledifferences in the definitions may lead to dramatically different physicalinterpretations of the results. Here, this statement is demonstrated for thecase of RSA of dimers on binary alloys.Comment: 20 pages, 8 figure

Fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media