  A vicious walker system consists of N random walkers on a line with any two
walkers annihilating each other upon meeting. We study a system of N vicious
accelerating walkers with the velocity undergoing Gaussian fluctuations, as
opposed to the position. We numerically compute the survival probability
exponent, {\alpha}, for this system, which characterizes the probability for
any two walkers not to meet. For example, for N = 3, {\alpha} = 0.71 \pm 0.01.
Based on our numerical data, we conjecture that 1/8N(N - 1) is an upper bound
on {\alpha}. We also numerically study N vicious Levy flights and find, for
instance, for N = 3 and a Levy index {\mu} = 1 that {\alpha} = 1.31 \pm 0.03.
Vicious accelerating walkers relate to no-crossing configurations of
semiflexible polymer brushes and may prove relevant for a non-Markovian
extension of Dyson's Brownian motion model.
