Duality has proved to be a powerful technique in the study of
interacting particle systems (IPS). This concept can be enlarged and a
“quasi-duality” defined between various pairs of IPS previously
thought unrelated. Consequently, theorems of a similar style to those involving
duality can be deduced.
¶ The concept of quasi-duality follows naturally from our previous
studies into the use of “single-site operators” (an idea borrowed
from quantum physics) in paper II of this series. It is shown that a necessary
condition for quasi-duality is that the eigenvalues of the corresponding
two-site infinitesimal generators be the same, and, using this observation, a
number of quasi-dual pairs have been found and studied.
¶ It is further shown that if two different IPS share a common dual,
then one can be considered as a “thinning” of the other.