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A central limit theorem for unbalanced step-reinforced random walks
Zhishui Hu, Liang Dong
https://arxiv.org/abs/2510.10898 https://arxiv.org/pdf/2510.1089…

A central limit theorem for unbalanced step-reinforced random walks
In this paper, we study a class of unbalanced step-reinforced random walks that unifies the elephant random walk, the positively step-reinforced random walk, and the negatively step-reinforced random walk. By establishing a connection with bond percolation on random recursive trees, these processes can be represented as randomly weighted sums of independent and identically distributed random variables. We first derive normal and stable central limit theorems for such randomly weighted sums, and…

Remoteness, order, size and connectivity constraints in digraphs
Sufiyan Mallu
https://arxiv.org/abs/2510.08841 https://arxiv.org/pdf/2510.08841

Remoteness, order, size and connectivity constraints in digraphs
Let \( D \) be a strongly connected digraph. The average distance of a vertex \( v \) in \( D \) is defined as the arithmetic mean of the distances from \( v \) to all other vertices in \( D \). The remoteness \( ρ(D) \) of \( D \) is the maximum of the average distances of the vertices in \( D \). In this paper, we provide a sharp upper bound on the remoteness of a strong digraph with given order, size, and vertex-connectivity. We then characterise the extremal digraphs that maximise remote…

Hobie and Rocky
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Season 1 Episode 22 "The End?"
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Rah ./generic/randombytes.c:29:10: fatal error: 'linux/random.h' file not found

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Season 1 Episode 11 "Shelter Me"
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Season 6 Episode 15 "Bash at the Beach"
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