Random Matrix Theory

Random Matrix Theory and Networks Workshop

Izaak Neri will be a scientific coordinator of the virtual workshop organized at MPI, that aims to bring together researchers working on random matrix theory and complex systems. 7-18 June 2021. Apply!

Counting equilibria in complex systems via random matrices

**Yan Fyodorov** discuss the number and stability properties of equilibria in large complex systems in a series of lectures given at the Park City Mathematics Institute.

Random matrices: Theory and Practice

**Pierpaolo Vivo** gives brief course on random matrix theory given at ICTP Trieste, from the theoretical foundations to applications to complex systems.

Physical Systems

In the domain of physical systems, the question of how to pack spheres optimally is familiar from everyday examples such as a greengrocer’s stack of oranges. But what if the spheres have a range of sizes, as happens for example in colloidal suspensions?

Protein interaction network

The definition and generation of good null models to assess the statistical relevance of observed features in protein interaction networks (PIN) is a well known problem in systems biology, where the aim is to understand how the structure of PINs relates to their biological functionality.

Sparse Symmetric Random Matrices

A collaboration between group members prof. Reimer Kuehn and Dr. Perez Castillo and international collaborators also led to a breakthrough in the spectral problem for sparse symmetric random matrices, allowing to efficiently compute spectral densities of such systems in the limit of large matrix size to any desired accuracy – more than 20 years after a solution to this problem was first attempted.

Universal Glassy Low-Temperature Anomalies

Prof. Reimer Kühn has provided the first formulation of a microscopic model to describe the emergence of the universal glassy low-temperature anomalies, including an understanding of the origin of the mysterious so-called quantitative universality – a problem that had been open since its formulation in the late 80s.