The spectrum of directed inhomogeneous random graphs follows a non-homogeneous circular law, with finite-rank outliers exhibiting explicit Gaussian fluctuations at scale sqrt(s_n/n).
Lecture Notes on "Free Probability Theory"
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This in an introduction to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. The material is mainly based on the two books of the lecturer, one joint with Nica and one joint with Mingo. Free probability is here restricted to the scalar-valued setting, the operator-valued version is treated in the subsequent lecture series on "Non-Commutative Distributions". The material here was presented in the winter term 2018/19 at Saarland University in 26 lectures of 90 minutes each. The lectures were recorded and can be found online at https://www.youtube.com/playlist?list=PLY11JnnnTUCYZni2Q7QNVa9hPGu77GK4M
fields
math.PR 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Spectrum of Directed Inhomogeneous Random Graphs
The spectrum of directed inhomogeneous random graphs follows a non-homogeneous circular law, with finite-rank outliers exhibiting explicit Gaussian fluctuations at scale sqrt(s_n/n).