Characteristic Power Series of Graph Limits

06/13/2019
by   Joshua N. Cooper, et al.
0

In this note, we show how to obtain a "characteristic power series" of graphons -- infinite limits of graphs -- as the limit of normalized reciprocal characteristic polynomials. This leads to a characterization of graph quasi-randomness and another perspective on spectral theory for graphons, including a complete description of the function in terms of the spectrum of the graphon as a self-adjoint kernel operator.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/30/2023

Self-normalized partial sums of heavy-tailed time series

We study the joint limit behavior of sums, maxima and ℓ^p-type moduli fo...
research
06/28/2021

Computing Characteristic Polynomials of p-Curvatures in Average Polynomial Time

We design a fast algorithm that computes, for a given linear differentia...
research
06/07/2023

Limits, approximation and size transferability for GNNs on sparse graphs via graphops

Can graph neural networks generalize to graphs that are different from t...
research
04/06/2019

X-Ramanujan Graphs

Let X be an infinite graph of bounded degree; e.g., the Cayley graph of ...
research
03/07/2020

Quasi-random words and limits of word sequences

Words are sequences of letters over a finite alphabet. We study two inti...
research
09/08/2023

The Randomness Deficiency Function and the Shift Operator

Almost surely, the difference between the randomness deficiencies of two...
research
07/16/2023

Weighted Graph Coloring for Quantized Computing

We consider the problem of distributed lossless computation of a functio...

Please sign up or login with your details

Forgot password? Click here to reset