Central limit theorems for high dimensional lattice polytopes: cosmological polytopes
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918518201516032 |
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| author | Donzelmann, Torben Juhnke, Martina Rednoß, Benedikt Thäle, Christoph |
| author_facet | Donzelmann, Torben Juhnke, Martina Rednoß, Benedikt Thäle, Christoph |
| contents | We study cosmological polytopes induced by Erdős--Rényi random graphs in a high-dimensional regime. These graph-based lattice polytopes form a natural model of random lattice polytopes in which geometric features are determined by the structure of the underlying random graph. Focusing on the number of polytope edges and on the number of edges in unimodular triangulations, we derive asymptotic formulas for expectations and variances and prove quantitative central limit theorems in the relevant parameter regime. The analysis relies on explicit graph-theoretic descriptions of the corresponding edge sets and on the discrete Malliavin--Stein method for normal approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23371 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Central limit theorems for high dimensional lattice polytopes: cosmological polytopes Donzelmann, Torben Juhnke, Martina Rednoß, Benedikt Thäle, Christoph Combinatorics Probability 52B20 (Primary) 52B05, 05C80, 60D05, 60F05 (Secondary) We study cosmological polytopes induced by Erdős--Rényi random graphs in a high-dimensional regime. These graph-based lattice polytopes form a natural model of random lattice polytopes in which geometric features are determined by the structure of the underlying random graph. Focusing on the number of polytope edges and on the number of edges in unimodular triangulations, we derive asymptotic formulas for expectations and variances and prove quantitative central limit theorems in the relevant parameter regime. The analysis relies on explicit graph-theoretic descriptions of the corresponding edge sets and on the discrete Malliavin--Stein method for normal approximation. |
| title | Central limit theorems for high dimensional lattice polytopes: cosmological polytopes |
| topic | Combinatorics Probability 52B20 (Primary) 52B05, 05C80, 60D05, 60F05 (Secondary) |
| url | https://arxiv.org/abs/2605.23371 |