Given the adjacency matrix of an undirected graph, we define a coupling of the spectral measures at the vertices, whose moments count the rooted closed paths in the graph. The resulting joint spectral measure verifies numerous interesting properties that allow to recover minors of analytic functions of the adjacency matrix from its generalized moments. We prove an extension of Obata’s Central Limit Theorem in growing star-graphs to the multivariate case and discuss some combinatorial properties using Viennot’s heaps of pieces point of view.
@article{10_37236_8674,
author = {Thibault Espinasse and Paul Rochet},
title = {A coupling of the spectral measures at a vertex},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8674},
zbl = {1417.05117},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8674/}
}
TY - JOUR
AU - Thibault Espinasse
AU - Paul Rochet
TI - A coupling of the spectral measures at a vertex
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8674/
DO - 10.37236/8674
ID - 10_37236_8674
ER -
%0 Journal Article
%A Thibault Espinasse
%A Paul Rochet
%T A coupling of the spectral measures at a vertex
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8674/
%R 10.37236/8674
%F 10_37236_8674
Thibault Espinasse; Paul Rochet. A coupling of the spectral measures at a vertex. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8674
