Geodesic
Large deviations for level sets of branching Brownian motion and Gaussian free fields
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 12-36

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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 [10]. 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. 
@article{ZNSL_2017_457_a2,
     author = {E. A{\"\i}d\'ekon and Yueyun Hu and Zhan Shi},
     title = {Large deviations for level sets of branching {Brownian} motion and {Gaussian} free fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {12--36},
     publisher = {mathdoc},
     volume = {457},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a2/}
}
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E. Aïdékon; Yueyun Hu; Zhan Shi. Large deviations for level sets of branching Brownian motion and Gaussian free fields. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 12-36. http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a2/