Singularly perturbed discrete differential equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910060653838336 |
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| author | Drmota, Michael Hainzl, Eva-Maria |
| author_facet | Drmota, Michael Hainzl, Eva-Maria |
| contents | Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$ but $k> 1$ for $x\ne 0$. We call such equations singularly perturbed. The main contribution of this work is to show that there is actually a smooth transition under certain natural assumptions. As an application of this result we consider pattern counts in triangular planar maps and derive a central limit theorem for patterns which cannot self-intersect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19484 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singularly perturbed discrete differential equations Drmota, Michael Hainzl, Eva-Maria Combinatorics Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$ but $k> 1$ for $x\ne 0$. We call such equations singularly perturbed. The main contribution of this work is to show that there is actually a smooth transition under certain natural assumptions. As an application of this result we consider pattern counts in triangular planar maps and derive a central limit theorem for patterns which cannot self-intersect. |
| title | Singularly perturbed discrete differential equations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.19484 |