  The properties of the host galaxies of a well-defined sample of 2215
radio-loud AGN with redshifts 0.03 < z < 0.3, defined from the SDSS, are
investigated. These are predominantly low radio luminosity sources, with 1.4GHz
luminosities of 10^23 to 10^25 W/Hz. The fraction of galaxies that host
radio-loud AGN with L(1.4GHz) > 10^23 W/Hz is a strong function of stellar
mass, rising from nearly zero below a stellar mass of 10^10 Msun to more than
30% at 5x10^11 Msun. The integral radio luminosity function is derived in six
ranges of stellar and black hole mass. Its shape is very similar in all of
these ranges and can be well fitted by a broken power-law. Its normalisation
varies strongly with mass, as M_*^2.5 or M_BH^1.6; this scaling only begins to
break down when the predicted radio-loud fraction exceeds 20-30%. There is no
correlation between radio and emission line luminosities for the radio-loud AGN
in the sample and the probability that a galaxy of given mass is radio-loud is
independent of whether it is optically classified as an AGN. The host galaxies
of the radio-loud AGN have properties similar to those of ordinary galaxies of
the same mass.
  All of these findings support the conclusion that the optical AGN and low
radio luminosity AGN phenomena are independent and are triggered by different
physical mechanisms. Intriguingly, the dependence on black hole mass of the
radio-loud AGN fraction mirrors that of the rate at which gas cools from the
hot atmospheres of elliptical galaxies. It is speculated that gas cooling
provides a natural explanation for the origin of the radio-loud AGN activity,
and it is argued that AGN heating could plausibly balance the cooling of the
gas over time. [Abridged]
