no code implementations • 7 Dec 2020 • Xinxin Chen, Christophe Garban, Atul Shekhar
In this work, we characterize all the point processes $\theta=\sum_{i\in \mathbb{N}} \delta_{x_i}$ on $\mathbb{R}$ which are left invariant under branching Brownian motions with critical drift $-\sqrt{2}$.
Point Processes Probability Mathematical Physics Mathematical Physics
no code implementations • 7 Dec 2020 • Xinxin Chen, Christophe Garban, Atul Shekhar
In this note, we give a new proof of Liggett's theorem on the invariant measures of independent particle systems from [Lig78] in the particular case of independent drifted Brownian motions.
Probability Mathematical Physics Mathematical Physics
no code implementations • 2 Dec 2020 • Christophe Garban, Avelio Sepúlveda
Finally, we transfer the above vortex fluctuations via a duality identity to the integer-valued GFF by showing that its maximum deviates in a quantitative way from the maximum of a usual GFF.
Probability Mathematical Physics Mathematical Physics 60K35, 82B20, 60B15, 60D05, 82B28