Marked GUE-corners process in doubly periodic dimer models
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917368478826496 |
|---|---|
| author | Berggren, Tomas Bradinoff, Nedialko |
| author_facet | Berggren, Tomas Bradinoff, Nedialko |
| contents | We study a family of periodically weighted Aztec diamond dimer models near their turning points. We establish that, asymptotically, as $N\rightarrow\infty$, their fluctuations there, scaled by $\sqrt{N}$, are described by a marked GUE-corners process. This limiting point process is constructed by assigning a Bernoulli mark independently to each particle in a realization of the GUE-corners process. The Bernoulli parameters associated with the random marks reflect the periodicity of the model in the limit. To prove this result we use a double-contour integral representation of the inverse Kasteleyn matrix on a higher-genus Riemann surface, which is well-suited for asymptotic analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27906 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Marked GUE-corners process in doubly periodic dimer models Berggren, Tomas Bradinoff, Nedialko Probability Mathematical Physics 60G55, 60B10 We study a family of periodically weighted Aztec diamond dimer models near their turning points. We establish that, asymptotically, as $N\rightarrow\infty$, their fluctuations there, scaled by $\sqrt{N}$, are described by a marked GUE-corners process. This limiting point process is constructed by assigning a Bernoulli mark independently to each particle in a realization of the GUE-corners process. The Bernoulli parameters associated with the random marks reflect the periodicity of the model in the limit. To prove this result we use a double-contour integral representation of the inverse Kasteleyn matrix on a higher-genus Riemann surface, which is well-suited for asymptotic analysis. |
| title | Marked GUE-corners process in doubly periodic dimer models |
| topic | Probability Mathematical Physics 60G55, 60B10 |
| url | https://arxiv.org/abs/2603.27906 |