Yanjia Bai and Lisa B. Hartung Refined Large Deviation Principle for Branching Brownian Motion Having a Low Maximum 2021 https://arxiv.org/abs/2102.09513
Maximillian Fels and Lisa B. Hartung Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Extremal process in the weakly correlated regime 2020 https://arxiv.org/abs/2002.00925
Maximilian Fels and Lisa B. Hartung Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Convergence of the maximum in the regime of weak correlations 2020 https://arxiv.org/abs/1912.13184
2018
Anton Bovier and Lisa B. Hartung From $1$ to $6$: a finer analysis of perturbed branching Brownian motion 2018 https://arxiv.org/abs/1808.05445
Anton Bovier and Lisa B. Hartung Variable speed branching Brownian motion 1. Extremal processes in the weak correlation regime Lat. Am. J. Probab. Math. Stat., 12(1): 261-291 2015 http://alea.impa.br/articles/v12/12-11.pdf
Abstract: We prove the convergence of the extremal processes for variable speed
branching Brownian motions where the ”speed functions”, that describe the timeinhomogeneous
variance, lie strictly below their concave hull and satisfy a certain
weak regularity condition. These limiting objects are universal in the sense that
they only depend on the slope of the speed function at 0 and the final time t.
The proof is based on previous results for two-speed BBM obtained in Bovier and
Hartung (2014) and uses Gaussian comparison arguments to extend these to the
general case.
Lisa B. Hartung and Anton Klimovsky The glassy phase of the complex branching Brownian motion energy model Electron. Commun. Probab., 20(Art. 78): 1-15 2015 http://dx.doi.org/10.1214/ECP.v20-4360
2014
Anton Bovier and Lisa B. Hartung The extremal process of two-speed branching Brownian motion Electron. J. Probab., 19(Art. 18): 1-28 2014 http://dx.doi.org/10.1214/EJP.v19-2982
Abstract: We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni \citeFZ_BM, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is \(\sigma_1\) for \(s\leq bt\) and \(\sigma_2\) when \(bt\leq s\leq t\). In the case \(\sigma_1>\sigma_2\), the process is the concatenation of two BBM extremal processes, as expected. In the case \(\sigma_1<\sigma_2\), a new family of cluster point processes arises, that are similar, but distinctively different from the BBM process. Our proofs follow the strategy of Arguin, Bovier, and Kistler.
Anton Bovier and Lisa B. Hartung Extended Convergence of the Extremal Process of Branching Brownian Motion ArXiv e-prints 2014 http://arxiv.org/abs/1412.5975
Abstract: We extend the results of Arguin et al and A\"\i{}d\'ekon et al on the convergence of the extremal process of branching Brownian motion by adding an extra dimension that encodes the "location" of the particle in the underlying Galton-Watson tree. We show that the limit is a cluster point process on R+×R where each cluster is the atom of a Poisson point process on R+×R with a random intensity measure Z(dz)×Ce−2√x, where the random measure is explicitly constructed from the derivative martingale. This work is motivated by an analogous conjecture for the Gaussian free field by Biskup and Louidor.