By Rongfeng SUN, National University of Singapore
The lonely branching random walks on Z^d is an interacting particle system where each particle moves as an independent random walk and undergoes critical binary branching when it is alone. It has been conjectured that in dimensions 1 and 2, the lonely branching random walks die out locally. We prove this conjecture and show furthermore that the same result holds if additional branching is allowed when the walk is not alone.
Joint work with Matthias Birkner.