Large deviations for level sets of branching Brownian motion and Gaussian free fields
Probability
2019-08-22 v2
Abstract
We study deviation probabilities for the number of high positioned particles in branching Brownian motion, and confirm a conjecture of Derrida and Shi (2016). 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.
Keywords
Cite
@article{arxiv.1710.00348,
title = {Large deviations for level sets of branching Brownian motion and Gaussian free fields},
author = {Elie Aïdékon and Yueyun Hu and Zhan Shi},
journal= {arXiv preprint arXiv:1710.00348},
year = {2019}
}
Comments
Dedicated to the memory of Professor V.N. Sudakov. The project was partly supported by ANR MALIN; E.A. also acknowledges supports from ANR GRAAL and ANR Liouville. This version corrects a mistake in the original version