Transitive closure in a polluted environment
We introduce a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap percolation, and percolation in polluted environments. We start with a collection of logical statements and known implications, as represented by an oriented graph G on n vertices. Then we attempt to logically complete the knowledge by transitivity, however, a censor places restrictions, represented by open and closed directed edges. We show that if G is a connected graph of bounded degree, and all other edges are open independently with probability p, then the transition between sparse and full completion of open edges occurs at p_c = (log n)^{-1/2+o(1)}. Joint work with Janko Gravner.
Date: 10 October 2022, 12:00 (Monday, 1st week, Michaelmas 2022)
Venue: Mathematical Institute, Woodstock Road OX2 6GG
Venue Details: L1
Speaker: Brett Kolesnik (University of Oxford)
Organising department: Department of Statistics
Organiser: Christina Goldschmidt (Department of Statistics, University of Oxford)
Organiser contact email address:
Part of: Probability seminar
Booking required?: Not required
Audience: Public
Editor: Christina Goldschmidt