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}
}
  • A. Bovier, Lisa Hartung
  • 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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    References

    SHOWING 1-10 OF 35 REFERENCES
    The extremal process of two-speed branching Brownian motion
    • 29
    • PDF
    Slowdown in branching Brownian motion with inhomogeneous variance
    • 37
    • PDF
    The extremal process of branching Brownian motion
    • 120
    • PDF
    Maximal displacement of branching brownian motion
    • 380
    • Highly Influential
    The genealogy of extremal particles of Branching Brownian Motion
    • 81
    • PDF