2012/09/30 by Roberts, Matthew I.
#60J80 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1210.0250
It is well-known that the maximal particle in a branching Brownian motion sits near √2 t - (3)/(2√2)log t at time t. One may then ask about the paths of particles near the frontier: how close can they stay to this critical curve? Two different approaches to this question have been developed. We improve upon the best-known bounds in each case, revealing new qualitative features including marked differences between the two approaches.