  The current paper is devoted to the study of existence and non-existence of
transition fronts for two species competition lattice system in random media,
and explore the influence of randomness of the media on the wave profiles and
wave speeds of such transition fronts. We first establish comparison principle
for sub-solutions and super-solutions of the related cooperative system. Next,
under some proper assumptions, we construct appropriate sub-solutions and
super-solutions for the cooperative system. Finally, we show that random
transition fronts exist if their least mean speed is greater than an explicit
threshold and there is no random transition front with least mean speed less
than the threshold.
