演講公告

新聞標題：　( 2017-02-14 )

• 演講主題：Scaling limits of random P\'olya trees

• 主講人：Emma Yu Jin (Technical University of Vienna)

• 演講日期：2017 年2月21日(星期二) 下午2:20 –3:05

• 演講地點：(光復校區) 科學一館223室

• 茶會時間：當天下午3:10 (科學一館205室)

• 摘要內容：
  

  A P\'olya tree is a rooted unlabeled tree considered up to symmetry. In 2015 Panagiotou and Stufler proved one important fact on their way to establish the scaling limit of random P\'olya trees: a uniform random P\'olya tree of size $n$ consists of a conditioned Galton-Watson tree $C_n$ and many small forests, where with probability tending to one as $n$ tends to infinity, any forest $F_n(v)$, that is attached to a node $v$ in $C_n$, is maximally of size $|F_n(v)|=O(\log n)$. Their proof used the framework of a Boltzmann sampler and deviation inequalities.
  In this talk, first I will review the enumeration and asymptotic estimation for the number of P\'olya trees. Second I present our main results on random P\'olya trees. The first one is an improvement on the bound $|F_n(v)|$, namely we prove $|F_n(v)|=\Theta(\log n)$ by employing a unified framework in analytic combinatorics. The second one is a combinatorial interpretation of the rational weights of these forests and the defining substitution process in terms of automorphisms associated to a given P\'olya tree. The third one is the limit probability that for a random node $v$, the attached forest $F_n(v)$ is of a given size.

• 相關檔案：Talk_1060221.pdf

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