Complex networks with tuneable dimensions as a universality playground

by Defenu Nicolò (ETH Zurich)

Wednesday 28 Apr 2021, 14:30 → 15:30 Europe/Rome

Universality is one of the key concepts in understanding
critical phenomena. However, for interacting inhomogeneous systems and
complex networks a clear understanding of the relevant parameters for
universality is often missing. To explore the role of dimension, we
construct a complex network model where the probability of a bond
between two nodes is proportional to a power law of the nodes' distance.
By explicit computation we prove that the spectral dimension for this
model can be tuned continuously from 1 to infinity, and we discuss
related network connectivity measures. We present a platform to explore
universal critical behavior in fractional dimension on inhomogeneous
structures, which can be realized experimentally in atomic, molecular
and optical devices