  We derive herein the limiting laws for certain stationary distributions of
birth-and-death processes related to the classical model of chemical
adsorption-desorption reactions due to Langmuir. The model has been recently
considered in the context of a hybridization reaction on an oligonucleotide DNA
microarray. Our results imply that the truncated gamma- and beta- type
distributions can be used as approximations to the observed distributions of
the fluorescence readings of the oligo-probes on a microarray. These findings
might be useful in developing new model-based, probe-specific methods of
extracting target concentrations from array fluorescence readings.
