The maximum-entropy median-martingale
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915993277693952 |
|---|---|
| author | Shah, Rikhav Winstein, Vilas |
| author_facet | Shah, Rikhav Winstein, Vilas |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03206 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The maximum-entropy median-martingale Shah, Rikhav Winstein, Vilas Probability 60G48, 60G07, 60G10 G.3 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. |
| title | The maximum-entropy median-martingale |
| topic | Probability 60G48, 60G07, 60G10 G.3 |
| url | https://arxiv.org/abs/2605.03206 |