Seminario Teoría de Números UAM-ICMAT

THE ZERO SET OF THE INDEPENDENCE POLYNOMIAL OF A GRAPH

SPEAKER: Martín Sombra (ICREA & UB)

DATE: Tuesday, 29th January 2019 - 11:30

VENUE: Aula 520, Módulo 17, Departamento de Matemáticas, UAM

ORGANISER: UAM - ICMAT

ABSTRACT: In statistical mechanics, the independence polynomial of a
graph G arises as the partition function of the hard-core lattice gas model
on G. The distribution of the zeros of these polynomials when G → ∞ is
relevant for the study of this model and, in particular, for the
determination of its phase transitions.
In this talk, I will review the known results on the location of these zeros,
with emphasis on the case of rooted regular trees of fixed degree and
varying depth k ≥ 0. Our main result states that for these graphs, the zero
sets of their independence polynomials converge as k → ∞ to the
bifurcation measure of a certain family of dynamical systems on the
Riemann sphere.
This is ongoing work with Juan Rivera-Letelier (Rochester).