Optimization-Free Concentrated Matrix-Exponentials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917445584814080 |
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| author | Battagliola, Maria Laura Peralta, Oscar |
| author_facet | Battagliola, Maria Laura Peralta, Oscar |
| contents | Near-deterministic positive delays require highly concentrated distributions, but phase-type models are constrained by the Erlang variance limit. While matrix-exponential distributions can empirically bypass this barrier, prior low-variance constructions relied entirely on numerical optimization. We propose an explicit family of concentrated matrix-exponential densities for the unit delay, obtained by raising the trigonometric Fejér kernel to logarithmic power. With exact moments and closed-form parameters, this gives the first analytical proof of a matrix-exponential class that asymptotically surpasses the Erlang bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26304 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimization-Free Concentrated Matrix-Exponentials Battagliola, Maria Laura Peralta, Oscar Probability Numerical Analysis Near-deterministic positive delays require highly concentrated distributions, but phase-type models are constrained by the Erlang variance limit. While matrix-exponential distributions can empirically bypass this barrier, prior low-variance constructions relied entirely on numerical optimization. We propose an explicit family of concentrated matrix-exponential densities for the unit delay, obtained by raising the trigonometric Fejér kernel to logarithmic power. With exact moments and closed-form parameters, this gives the first analytical proof of a matrix-exponential class that asymptotically surpasses the Erlang bound. |
| title | Optimization-Free Concentrated Matrix-Exponentials |
| topic | Probability Numerical Analysis |
| url | https://arxiv.org/abs/2604.26304 |