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The fixed points of Branching Brownian Motion
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
A new proof of Liggett's theorem for non-interacting Brownian motions
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
Quantitative bounds on vortex fluctuations in $2d$ Coulomb gas and maximum of the integer-valued Gaussian free field
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
