In the last two decades, the classical Arrow and Debreu result on the existence of Walrasian equilibria has been generalized in many directions. Mas-Colell has first shown that the existence of an equilibrium can be established without assuming preferences to be total or transitive. Next, by using an existence theorem of maximal elements, Gale and Mas-Colell gave a proof of the existence of a competitive equilibrium without ordered preferences. By using Kakutani's fixed point theorem, Shafer and Sonnenschein proved a powerful result on the ``Arrow and Debreu Lemma'' for abstract economies in which preferences may not be total or transitive but have open graphs. Meanwhile, Borglin and Keiding proved a new existence theorem for a compact abstract economy with KF-majorized preference correspondences. Following their ideas, there have been a number of generalizations of the existence of equilibria for compact abstract economies. These theorems generalized most known equilibrium existence theorems on compact generalized games due to Borglin and Keiding, Shafer and Sonnenschein, Toussaint, and Yannelis and Prabhakar. On the other hand, Debreu discussed the uncertainty of behavior of an economic activity and a series of papers concerning the uncertainty of behavior of economic actions have followed. For example, Hildenbrand considered an economy in which the preferences are random correspondences; Bewley studied the existence of equilibrium in abstract economies with a measure space of agents and with an infinite-dimensional strategy space; Kim et al. also proved the existence of equilibria in abstract economies with a measure space of agents and with an infinite-dimensional strategy space by random fixed point theorems. In this paper, the existence theorems of non-compact random equilibria in which the preference correspondences are \(L\)-majorized and constraint correspondences are upper semicontinuous are first obtained. As applications, we give the existence theorems for non-compact random quasi-variational inequalities, which in turn imply several existence theorems for non-compact generalized random quasi-variational inequalities. These results not only generalize the results of Tan and Zhang, but also are the stochastic versions of corresponding results in the literature.