Dear Colleagues, We are pleased to invite you to the following SPASS seminar (jointly organised by UniPi, SNS, and UniFi): Speaker: Alessio Catanzaro (IMT Lucca) Title: Spectra of networks with Discrete Scale-Invariance Date and time: Tue 13th October at 12:00 Place: Aula Tricerri, DIMAI, University of Florence Join online: https://meet.google.com/iyq-wjvs-rvy On behalf of the organisers, Elia Bisi ********************* Abstract: In this talk, I will show results on the spectral properties of an infinitely renormalizable random network model. This model is an 'anti-benchmark’ for Random Matrix Theory techniques because many working assumptions fail, such as moment matching methods, the low rank hypothesis for the signal matrix, and the non-self-averaging nature of the ESD. Despite these challenges, I will show an ansatz for the eigenfunctions based on the Laplace transform of the weights distribution. This allows to solve the eigenvalue equation for the signal matrix, which is a good proxy for the largest eigenmodes of the network realisations. The leading eigenvalues are all of order √n, alternate in sign, and lie at the intersection between the real axis and a logarithmic spiral in the complex plane. I will also show haow to calculate the associated eigenvectors, which display complex-valued scaling exponents and log-periodicity, indicating discrete scale invariance. ————————— Elia Bisi Assistant Professor (RTT) University of Florence Department of Mathematics & Computer Science Personal homepage Florence Probability Group