Random matrices and condensation into multiple states.

In the present work, we employ methods from statistical mechanics of disordered systems to investigate static properties of condensation into multiple states in a general framework. We aim at showing how typical properties of random interaction matrices play a vital role in manifesting the statistics of condensate states. In particular, an analytical expression for the fraction of condensate states in the thermodynamic limit is provided that confirms the result of the mean number of coexisting species in a random tournament game. We also study the interplay between the condensation problem and zero-sum games with correlated random payoff matrices.