Projects per year
Personal profile
Research interests
Random Matrix Theory, Quantum Chaos and Statistical Mechanics
Random matrices are often used to study the statistical properties of systems whose detailed mathematical description is either not known or too complicated to allow any kind of successful approach. It is a remarkable fact that predictions made using random matrix theory have turned out to be accurate in a wide range of fields: statistical mechanics, quantum chaos, nuclear physics, quantum transport, number theory, combinatorics, wireless telecommunications, quantum field theory and probability, to name only few examples. My research has focused mainly on applications of random matrices to quantum transport, quantum chaos, statistical mechanics and on the universality properties of the statistics of the eigenvalues.
PhD Projects
I am open to supervise projects in most current areas of research in Random Matrix Theory. Interested students should contact me by email for enquiries, [email protected]. In particular, my interests include the following topics.
TwoDimensional One Component Plasma and NonHermitian Random Matrices
The joint probability density function of the eigenvalues of NonHermitian Matrices has the same form of the Boltzmann factor of a twodimensional plasma of Coulomb charges 2DOCP. This statistical mechanics fluid model has appeared in several areas of physics and mathematics. Indeed, the logarithmic repulsion of the charges occurs as interaction between vortices and dislocations in systems such as superconductors, superfluids, rotating BoseEinstein condensates. There is also an analogy between the 2DOCP and the Laughlin trial wave function in the theory of fractional quantum Hall effect. We can apply techniques from Random Matrix Theory to gain a better understanding of the behaviour of these systems. A PhD project can be chosen among many open problems in this areas. See Cunden, F.D., Mezzadri, F. & Vivo, P. “Large deviations of radial statistics in the twodimensional onecomponent plasma.” J Stat Phys (2016) 164: 1062. doi:10.1007/s109550161577x
Random Matrix Theory and Quantum Transport
Quantum transport in disordered mesoscopic conductors have important applications in modern technology, where it has become increasingly important to miniaturise components of electronic devices. In the 1980s it was discovered that the statistical fluctuations of the conductance in disordered quasi onedimensional wires are universal, which means that within certain limits they are independent of the size of the sample and strength of the disorder. Soon afterwards it was realised that Random Matrix Theory could provide the mathematical framework to develop a statistical theory of quantum transport that would account of the universality of the fluctuations of the electric current. Recently a lot progress in this area has been achieved exploiting the link between Random Matrix Theory and integrable systems. There are still many open questions that can be answered using these ideas and that can be chosen as a PhD project. See. Mezzadri, F. and Simm, N. J. “TauFunction Theory of Quantum Chaotic Transport with beta=1,2,4.” Commun. Math. Phys. (2013) 324: 465. doi:10.1007/s002200131813z
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Collaborations and top research areas from the last five years
Projects
 3 Finished
Research output

On the moments of characteristic polynomials
Jonnadula, B., Keating, J. P. & Mezzadri, F., 1 May 2023, In: Glasgow Mathematical Journal. 65, S1, p. S102  S122Research output: Contribution to journal › Article (Academic Journal) › peerreview
Open AccessFile2 Citations (Scopus)30 Downloads (Pure) 
A spinglass model for the loss surfaces of generative adversarial networks
Baskerville, N. P., Keating, J. P., Mezzadri, F. & Najnudel, J., 18 Jan 2022, In: Journal of Statistical Physics. 186, 2, 45 p., 29 .Research output: Contribution to journal › Article (Academic Journal) › peerreview
Open AccessFile6 Citations (Scopus)197 Downloads (Pure) 
On the number of real eigenvalues of a product of truncated orthogonal random matrices
Little, A., Mezzadri, F. & Simm, N., 14 Jan 2022, (Epub ahead of print) In: Electronic Journal of Probability. 27, p. 132 32 p., 5.Research output: Contribution to journal › Article (Academic Journal) › peerreview
Open AccessFile4 Citations (Scopus)36 Downloads (Pure)
Prizes

London Mathematical Society Fröhlich Prize
Mezzadri, Francesco (Recipient), 29 Jun 2018
Prize: Prizes, Medals, Awards and Grants
Thesis

Boundary conditions for torus maps and spectral statistics
Author: Mezzadri, F., 1999Supervisor: Keating, J. (Supervisor)
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)