LA Probability Forum

USC Kaprielian (KAP) 414

Fix a graph G and a starting vertex r (the root), and let T be a spanning tree of G grown as follows. Initially, vertex r is infected and all other vertices are susceptible. At constant rate, each infected node infects each neighbouring susceptible node. For s>0, the infection tree T_s is composed with the set of vertices that have been infected by time s, together with the set of edges along which the infection has spread. 

How easy is it to recover the identity of the initially infected individual r if one is given access to T_s for some (large) s? 

I will discuss recent work on this problem when G is a random graph with a fixed degree sequence, or G is a supercritical Bienaymé tree, or is the Poisson-weighted infinite tree (in which case the problem must be modified slightly). 

Based on joint work with Sasha Bell, Tasmin Chu, Théodore Conrad-Frenkiel, Catherine Fontaine, Robin Khanfir, Louis-Pierre Langevin, and Simone Têtu.