Word maps and random words
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910808410161152 |
|---|---|
| author | Breuillard, Emmanuel Glazer, Itay |
| author_facet | Breuillard, Emmanuel Glazer, Itay |
| contents | We discuss some recent results by a number of authors regarding word maps on algebraic groups and finite simple groups, their mixing properties and the geometry of their fibers, emphasizing the role played by equidistribution results in finite fields via recent advances on character bounds and non-abelian arithmetic combinatorics. In particular, we discuss character varieties of random groups. In the last section, we give a new proof of a recent theorem of Hrushovski about the geometric irreducibility of the generic fibers of convolutions of dominant morphisms to simply connected algebraic groups.
These notes stem out of lectures given by the authors in Oxford, and by the first author in ICTS Bangalore, in spring 2024. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Word maps and random words Breuillard, Emmanuel Glazer, Itay Group Theory Probability 14M35, 20P05 (Primary) 20D06, 20F69, 20F70, 20G15, 60B15 (Secondary) We discuss some recent results by a number of authors regarding word maps on algebraic groups and finite simple groups, their mixing properties and the geometry of their fibers, emphasizing the role played by equidistribution results in finite fields via recent advances on character bounds and non-abelian arithmetic combinatorics. In particular, we discuss character varieties of random groups. In the last section, we give a new proof of a recent theorem of Hrushovski about the geometric irreducibility of the generic fibers of convolutions of dominant morphisms to simply connected algebraic groups. These notes stem out of lectures given by the authors in Oxford, and by the first author in ICTS Bangalore, in spring 2024. |
| title | Word maps and random words |
| topic | Group Theory Probability 14M35, 20P05 (Primary) 20D06, 20F69, 20F70, 20G15, 60B15 (Secondary) |
| url | https://arxiv.org/abs/2502.00417 |