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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E. Aïdékon

LPMA, Université Pierre et Marie Curie

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Email: elie.aidekon@upmc.fr
法国, Paris

Yueyun Hu

LAGA, Université Paris XIII

Email: elie.aidekon@upmc.fr
法国, Villetaneuse

Zhan Shi

LPMA, Université Pierre et Marie Curie

Email: elie.aidekon@upmc.fr
法国, Paris

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