6 papers
A path integral approach to sparse non-Hermitian random matrices
Joseph W. Baron
The theory of large random matrices has proved an invaluable tool for the study of systems with disordered interactions in many quite disparate research areas. Widely applicable re…
Breakdown of random-matrix universality in persistent Lotka--Volterra communities
Joseph W. Baron, Thomas Jun Jewell, Christopher Ryder +1
The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The v…
Eigenvalues of random matrices with generalised correlations: a path integral approach
Joseph W. Baron, Thomas Jun Jewell, Christopher Ryder +1
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what fa…
Dispersal-induced instability in complex ecosystems
Joseph W. Baron, Tobias Galla
In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduc…
Generalised correlations in disordered dynamical systems: Insights from the many-species Lotka-Volterra model
Sebastian Holtedahl Castedo, Joshua Holmes, Joseph William Baron +1
In the study of disordered systems, one often chooses a matrix of independent identically distributed interaction coefficients to represent the quenched random couplings between co…
Interaction networks in persistent Lotka-Volterra communities
Lyle Poley, Tobias Galla, Joseph W. Baron
A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we…