Poisson approximation of random lattices
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917480606203904 |
|---|---|
| author | Klartag, Boaz |
| author_facet | Klartag, Boaz |
| contents | Fix a subset $S \subset \mathbb{R}^n$ of volume at most $c n$ that satisfies $S \cap (-S) = \emptyset$. We consider two point processes in $S$: the first is the Poisson point process of intensity one, and the second is the restriction of a random lattice to $S$, where the random lattice is distributed uniformly in the space of covolume-one lattices. We show that the total variation distance between these two point processes is at most $C e^{-c' n}$, where $c, C, c' > 0$ are universal constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10479 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Poisson approximation of random lattices Klartag, Boaz Probability Metric Geometry Number Theory Fix a subset $S \subset \mathbb{R}^n$ of volume at most $c n$ that satisfies $S \cap (-S) = \emptyset$. We consider two point processes in $S$: the first is the Poisson point process of intensity one, and the second is the restriction of a random lattice to $S$, where the random lattice is distributed uniformly in the space of covolume-one lattices. We show that the total variation distance between these two point processes is at most $C e^{-c' n}$, where $c, C, c' > 0$ are universal constants. |
| title | Poisson approximation of random lattices |
| topic | Probability Metric Geometry Number Theory |
| url | https://arxiv.org/abs/2605.10479 |