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Large Deviations for Level Sets of a Branching Brownian Motion and Gaussian Free Fields

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We study deviation probabilities for the number of high positioned particles in branching Brownian motion and confirm a conjecture of Derrida and Shi. We also solve the corresponding problem for the two-dimensional discrete Gaussian free field. Our method relies on an elementary inequality for inhomogeneous Galton–Watson processes.

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Authors and Affiliations

  1. LPMA, Université Pierre et Marie Curie, Paris, France

    E. Aïdékon & Zhan Shi

  2. LAGA, Université Paris XIII, Villetaneuse, France

    Yueyun Hu

Authors
  1. E. Aïdékon
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  2. Yueyun Hu
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  3. Zhan Shi
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Correspondence to E. Aïdékon.

Additional information

Dedicated to the memory of Professor V. N. Sudakov

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 457, 2017, pp. 12–36.

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Aïdékon, E., Hu, Y. & Shi, Z. Large Deviations for Level Sets of a Branching Brownian Motion and Gaussian Free Fields. J Math Sci 238, 348–365 (2019). https://doi.org/10.1007/s10958-019-04243-8

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  • DOI: https://doi.org/10.1007/s10958-019-04243-8

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