This paper has been withdrawn by Rafael Chiclana Vega
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Abstract:We study hitting times in simple random walks on graphs, which measure the time required to reach specific target vertices. Our main result establishes a sharp lower bound for the variance of hitting times. For a simple random walk on a graph with $n$ vertices, we prove that the variance of the hitting time from a vertex $x$ to a vertex $y$, denoted $\tau_y$, is at least of the order $\mathbb{E}_x(\tau_y)^2 / \log n$. When the graph is a tree, we show that $n$ can be replaced by the graph's distance between vertices $x$ and $y$.
From: Rafael Chiclana Vega [view email]
[v1]
Tue, 12 Dec 2023 20:42:13 UTC (7 KB)
[v2]
Fri, 22 Mar 2024 15:17:36 UTC (1 KB) (withdrawn)
[v3]
Mon, 1 Jun 2026 03:59:29 UTC (1 KB) (withdrawn)
[v4]
Tue, 14 Jul 2026 13:37:11 UTC (1 KB) (withdrawn)
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