# From $1$ to $6$: a finer analysis of perturbed branching Brownian motion.

@article{Bovier2018FromT,
title={From \$1\$ to \$6\$: a finer analysis of perturbed branching Brownian motion.},
author={A. Bovier and Lisa Hartung},
journal={arXiv: Probability},
year={2018}
}
• Published 2018
• Mathematics
• arXiv: Probability
• The logarithmic correction for the order of the maximum for two-speed branching Brownian motion changes discontinuously when approaching slopes $\sigma_1^2=\sigma_2^2=1$ which corresponds to standard branching Brownian motion. In this article we study this transition more closely by choosing $\sigma_1^2=1\pm t^{-\alpha}$ and $\sigma_2^2=1\pm t^{-\alpha}$. We show that the logarithmic correction for the order of the maximum now smoothly interpolates between the correction in the iid case \$\frac… CONTINUE READING
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