Can one hear the shape of a random walk?
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917114712948736 |
|---|---|
| author | Larsen, Michael J. |
| author_facet | Larsen, Michael J. |
| contents | To what extent is the underlying distribution of a finitely supported unbiased random walk on $\mathbb{Z}$ determined by the sequence of times at which the walk returns to the origin? The main result of this paper is that, in various senses, most unbiased random walks on $\mathbb{Z}$ are determined up to equivalence by the sequence $I_1,I_2,I_3,\ldots$, where $I_n$ denotes the probability of being at the origin after $n$ steps. We also give an application to an inverse problem from asymptotic representation theory. The proof uses Laplace's method and a delicate Galois-theoretic analysis which ultimately depends on the classification of finite simple groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Can one hear the shape of a random walk? Larsen, Michael J. Probability 60G50 (Primary) 58J53 (Secondary) To what extent is the underlying distribution of a finitely supported unbiased random walk on $\mathbb{Z}$ determined by the sequence of times at which the walk returns to the origin? The main result of this paper is that, in various senses, most unbiased random walks on $\mathbb{Z}$ are determined up to equivalence by the sequence $I_1,I_2,I_3,\ldots$, where $I_n$ denotes the probability of being at the origin after $n$ steps. We also give an application to an inverse problem from asymptotic representation theory. The proof uses Laplace's method and a delicate Galois-theoretic analysis which ultimately depends on the classification of finite simple groups. |
| title | Can one hear the shape of a random walk? |
| topic | Probability 60G50 (Primary) 58J53 (Secondary) |
| url | https://arxiv.org/abs/2412.19762 |