SEMINARIO
Probabilita'
Tyler Helmuth
(University of Bristol)
Titolo: Random spanning forests and hyperbolic symmetry
Giovedi' 12 Dicembre 2019 ORE 10:00
Dipartimento di Matematica e Fisica
Universita' degli Studi Roma Tre
Largo San Leonardo Murialdo,1 - Pal.C - Aula 211
Abstract
The arboreal gas is a probability measure that arises from
conditioning the random subgraph given by Bernoulli(p) bond
percolation to be a spanning forest, i.e., to contain no cycles. This
conditioning makes sense on any finite graph G, and specializes to the
uniform measure on spanning forests when p = 1/2. One is naturally
lead to ask about the percolative properties of the arboreal gas, and
this turns out to be a surprisingly rich question. I will discuss some
results and conjectures about the arboreal gas, most of which are
based on important relations between the arboreal gas and spin systems
with hyperbolic symmetry.
Based on joint work in progress with Roland Bauerschmidt, Nick
Crawford, and Andrew Swan.