Work

Tree walks and the spectrum of random graphs

Year: 2026

Type: article

Abstract: It is a classic result in spectral graph theory that the empirical spectral measure of random graphs G ( n , p ) converges to the semicircle law in case n p tends to infinity with n . The spectral measure for random graphs G ( n , c / n ) however is less understood. In this work, we combine and extend two combinatorial approaches due to Bauer and Golinelli (2001) and Enriquez and Ménard (2016) and approximate the expected moments of the spectral measure by counting closed walks that span trees.

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2026.104386

Authors: Eva-Maria Hainzl, Élie de Panafieu

Institutions: TU Wien, Nokia (France)

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Austrian Science Fund, HORIZON EUROPE Marie Sklodowska-Curie Actions

Awards: G4224269593, G4790733421