Abstract
We study the overlap distribution of two particles chosen under the Gibbs measure at two temperatures for the branching Brownian motion. We first prove the convergence of the overlap distribution using the extended convergence of the extremal process obtained by Bovier and Hartung [8]. We then prove that the mean overlap of two points chosen at different temperatures is strictly smaller than in Derrida’s random energy model. The proof of this last result is achieved with the description of the decoration point process obtained by Aïdékon, Berestycki, Brunet and Shi [1]. To our knowledge, it is the first time that this description is being used.
Acknowledgments
I wish to thank my supervisor Olivier Zindy for introducing me to this subject and for useful discussions. I would like to also thank Zhan Shi for explaining precisely to me the description of the distribution of the decoration process obtained in [1].
Citation
Benjamin Bonnefont. "The overlap distribution at two temperatures for the branching Brownian motion." Electron. J. Probab. 27 1 - 21, 2022. https://doi.org/10.1214/22-EJP841
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