A Note on Maxima in Random Walks

Electronic Journal Of Combinatorics

Joseph Helfer¹ 

关键词: Dyck words;    Dyck paths;    Random walks;    Catalan numbers;   

DOI  :  

学科分类：离散数学和组合数学

来源: Electronic Journal Of Combinatorics

【 摘 要 】

We give a combinatorial proof that a random walk attains a unique maximum with probability at least $1/2$. For closed random walks with uniform step size, we recover Dwass's count of the number of length $\ell$ walks attaining the maximum exactly $k$ time

【 授权许可】

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