Height coupled trees | Vidéo | Carmin.tv

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Height coupled trees

By Meltem Ünel

Appears in collection : Random Geometry / Géométrie aléatoire

We consider planar rooted random trees whose distribution is even for fixed height $h$ and size $N$ and whose height dependence is of exponential form $e^{-\mu h}$. Defining the total weight for such trees of fixed size to be $Z^{(\mu)}_N$, we determine its asymptotic behaviour for large $N$, for arbitrary real values of $\mu$. Based on this we evaluate the local limit of the corresponding probability measures and find a transition at $\mu=0$ from a single spine phase to a multi-spine phase. Correspondingly, there is a transition in the volume growth rate of balls around the root as a function of radius from linear growth for $\mu<0$ to the familiar quadratic growth at $\mu=0$ and to cubic growth for $\mu> 0$.

Information about the video

Date of recording 20/01/2022
Date of publication 04/02/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19878603
Cite this video Ünel, Meltem (20/01/2022). Height coupled trees. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19878603
URL https://dx.doi.org/10.24350/CIRM.V.19878603

Domain(s)

Probability

Bibliography

DURHUUS, Bergfinnur et ÜNEL, Meltem. Trees with exponential height dependent weight. arXiv preprint arXiv:2112.06570, 2021. - https://arxiv.org/abs/2112.06570

MSC codes

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