4 papers
Tree Builder Random Walk: recurrence, transience and ballisticity
Giulio Iacobelli, Rodrigo Ribeiro, Glauco Valle +1
The Tree Builder Random Walk is a special random walk that evolves on trees whose size increases with time, randomly and depending upon the walker. After every s steps of the walke…
The end time of SIS epidemics driven by random walks on edge-transitive graphs
Daniel Figueiredo, Giulio Iacobelli, Seva Shneer
Network epidemics is a ubiquitous model that can represent different phenomena and finds applications in various domains. Among its various characteristics, a fundamental question…
Transient and Slim versus Recurrent and Fat: Random Walks and the Trees they Grow
Giulio Iacobelli, Daniel R. Figueiredo, Giovanni Neglia
Network growth models that embody principles such as preferential attachment and local attachment rules have received much attention over the last decade. Among various approaches,…
A note on counting labeled and unlabeled trees
Victor N. Ermolaev, Giulio Iacobelli
We provide a short combinatorial proof of Cayley's formula by means of a bijective map to an outcome space of an urn-drawing problem. Furthermore we introduce an algebraic structur…