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Journal of Mathematical Sciences

, Volume 238, Issue 4, pp 348–365 | Cite as

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

  • E. AïdékonEmail author
  • Yueyun Hu
  • Zhan Shi
Article
  • 3 Downloads

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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LPMA, Université Pierre et Marie CurieParisFrance
  2. 2.LAGA, Université Paris XIIIVilletaneuseFrance

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