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SUMMARY:Random trees conditioned on the number of vertices and leaves - Sl
 ava Kargin (Binghampton)
DTSTART:20230221T153000Z
DTEND:20230221T163000Z
UID:TALK197680@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:I will talk about Galton-Watson trees conditioned on both the 
 total number of vertices $n$ and the number of leaves $k$. Both $k$ and $n
 $ are assumed to grow to infinity and $k = \\alpha n + O(1)$\, with $\\alp
 ha \\in (0\, 1)$. Assuming the exponential decay of the offspring distribu
 tion\, I show that the rescaled random tree converges in distribution to A
 ldous' Continuum Random Tree with respect to the Gromov-Hausdorff topology
 . The rescaling depends on a parameter $\\sigma^2$ which can be calculated
  explicitly. Additionally\, I will describe the limit of the degree sequen
 ce for the conditioned trees.\n
LOCATION:MR12\, Centre for Mathematical Sciences
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