Instabilities in Complex Mixtures with a Large Number of Components

Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterize all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second-virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.