








Abstract:This short note explores the maximum-entropy walk on the unit interval that is a median-martingale. That is, the median of its next state is equal to its current state. The stationary distribution of this walk is the arcsine distribution, and we provide a proof that elucidates the connection to two classical arcsine laws for Brownian motion. The notion of a martingale is further generalized, and a larger class of walks is considered and similarly characterized.
From: Rikhav Shah [view email]
[v1]
Mon, 4 May 2026 22:50:00 UTC (7 KB)
[v2]
Fri, 8 May 2026 17:47:54 UTC (8 KB)
[v3]
Sun, 2 Aug 2026 20:31:31 UTC (10 KB)
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