The Range of a Simple Random Walk on $\mathbb{Z}$: An Elementary Combinatorial Approach

[摘要] Two different elementary approaches for deriving an explicit formula for the distribution of the range of a simple random walk on $\mathbb{Z}$ of length $n$ are presented. Both of them rely on Hermann Weyl's discrepancy norm, which equals the maximal part

[学科分类] 离散数学和组合数学

[关键词] random walk;discrepancy norm;lattice path enumeration