Slowdown for time inhomogeneous branching Brownian motion
  We consider the maximal displacement of one dimensional branching Brownian motion with (macroscopically) time varying profiles. For monotone decreasing variances, we show that the correction from linear displacement is not logarithmic but rather proportional to $T^{1/3}$. We conjecture that this is the worse case correction possible. 
Ming Fang, Ofer Zeitouni
math.PR