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Slowdown for Time Inhomogeneous Branching Brownian Motion

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences Xiamen, University Xiamen, Fujian, 361005, China

    Ming Fang

  2. Weizmann Institute, Rehovot, Israel

    Ofer Zeitouni

  3. University of Minnesota, Minneapolis, USA

    Ofer Zeitouni

Authors
  1. Ming Fang
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  2. Ofer Zeitouni
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Correspondence to Ofer Zeitouni.

Additional information

O. Zeitouni is partially supported by NSF grant #DMS-1106627 and by a grant from the Israel Science Foundation.

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Fang, M., Zeitouni, O. Slowdown for Time Inhomogeneous Branching Brownian Motion. J Stat Phys 149, 1–9 (2012). https://doi.org/10.1007/s10955-012-0581-z

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  • DOI: https://doi.org/10.1007/s10955-012-0581-z

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