The study of the eigenvalue spectra of random matrices in Physics was initiated by Wigner in the context of heavy nuclei in the 1950s. Since then, random matrix theory has found a diverse range of applications and has been a fruitful area of study in both Mathematics and Physics. In this talk, I will discuss two applications of the theory of random matrices. First, I will demonstrate how diffusion can be a destabilising influence in a model of a complex ecosystem. In this context, I will consider the eigenvalue spectra of random matrices with block structure -- a generalisation of Robert May's paradigmatic model introduced in the 1970s. Secondly, I will illustrate how quenched disorder can give rise to persistent individual bias in the voter model. In doing so, I will make use of techniques developed for the study of sparse random matrices. Such techniques have previously been used in the study of dilute spin systems.
Meeting ID: 838 2931 8876
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