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In biophysics and related fields, reduced dimension forms are unique on-off mechanisms for random walks that generate two-state trajectories. It has been shown that RDFs solve two-state trajectories, since only one RDF can be constructed from the data, where this property does not hold for on-off kinetic schemes, where many kinetic schemes can be constructed from a particular two-state trajectory. Two-state time trajectories are very common in measurements in chemistry, physics, and the biophysics of individual molecules , thus making RDFs an important tool in the analysis of data in these fields.
Since RDFs are uniquely obtained from the data, they have many advantages over other mathematical and statistical methods that were developed for solving two-state trajectories.