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- W3133538963 abstract "Let $T$ be the triangle in the plane with vertices $(0,0)$, $(0,1)$ and $(0,1)$. The convex hull of $(0,1)$, $(1,0)$ and $n$ independent random points uniformly distributed in $T$ is the random convex chain $T_n$. A three-term recursion for the probability generating function $G_n$ of the number $f_0(T_n)$ of vertices of $T_n$ is proved. Via the link to orthogonal polynomials it is shown that $G_n$ has precisely $n$ distinct real roots in $(-infty,0]$ and that the sequence $p_k^{(n)}:=mathbb{P}(f_0(T_n)=k)$, $k=1,ldots,n$, is a Polya frequency (PF) sequence. A selection of probabilistic consequences of this surprising and remarkable fact are discussed in detail." @default.
- W3133538963 created "2021-03-15" @default.
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- W3133538963 date "2021-02-25" @default.
- W3133538963 modified "2023-10-12" @default.
- W3133538963 title "ON RANDOM CONVEX CHAINS, ORTHOGONAL POLYNOMIALS, PF SEQUENCES AND PROBABILISTIC LIMIT THEOREMS" @default.
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- W3133538963 doi "https://doi.org/10.1112/mtk.12081" @default.
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