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Bibliographic Details
Main Authors: Shah, Rikhav, Winstein, Vilas
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.03206
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Table of Contents:
  • 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.