Français
Height coupled trees
Multi angle
Authors : Ünel, Meltem (Author of the conference)
CIRM (Publisher )
05C05 - Trees
60B10 - Convergence of probability measures
60J75 - Jump processes
CIRM (Publisher )
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Abstract :
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 $\mu> 0$.
Keywords : random trees; local limit; height dependent weights
MSC Codes : Keywords : random trees; local limit; height dependent weights
05C05 - Trees
60B10 - Convergence of probability measures
60J75 - Jump processes
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/02/2022 Conference Date : 20/01/2022 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:52:01 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-01-20_Unel.mp4 
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Information on the Event
Event Title : Random Geometry / Géométrie aléatoireEvent Organizers : Curien, Nicolas ; Goldschmidt, Christina ; Le Gall, Jean-François ; Miermont, Grégory ; Rhodes, Rémi Dates : 17/01/2022 - 21/01/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2528.html
Citation Data
DOI : 10.24350/CIRM.V.19878603Cite this video as: Ünel, Meltem (2022). Height coupled trees. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19878603 URI : http://dx.doi.org/10.24350/CIRM.V.19878603 |
See Also
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- [Multi angle] Unicellular maps vs hyperbolic surfaces in high genus / Author of the conference Louf, Baptiste.
- [Multi angle] Bijections for maps on non-oriented surfaces / Author of the conference Dołęga, Maciej.
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- [Multi angle] The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity / Author of the conference Borga, Jacopo.
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Bibliography
- DURHUUS, Bergfinnur et ÜNEL, Meltem. Trees with exponential height dependent weight. arXiv preprint arXiv:2112.06570, 2021. - https://arxiv.org/abs/2112.06570
Imagette Video
