التفاصيل البيبلوغرافية
| العنوان: |
Lozenge tilings and the Gaussian free field on a cylinder |
| المؤلفون: |
Andrew Ahn, Marianna Russkikh, Roger Van Peski |
| بيانات النشر: |
arXiv, 2021. |
| سنة النشر: |
2021 |
| مصطلحات موضوعية: |
Probability (math.PR), FOS: Mathematics, Mathematics - Combinatorics, FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Combinatorics (math.CO), Mathematics - Probability, Mathematical Physics |
| الوصف: |
We use the periodic Schur process, introduced in arXiv:math/0601019v1, to study the random height function of lozenge tilings (equivalently, dimers) on an infinite cylinder distributed under two variants of the $q^{\operatorname{vol}}$ measure. Under the first variant, corresponding to random cylindric partitions, the height function converges to a deterministic limit shape and fluctuations around it are given by the Gaussian free field in the conformal structure predicted by the Kenyon-Okounkov conjecture. Under the second variant, corresponding to an unrestricted dimer model on the cylinder, the fluctuations are given by the same Gaussian free field with an additional discrete Gaussian shift component. Fluctuations of the latter type have been previously conjectured for dimer models on planar domains with holes.
Comment: 43 pages, 6 figures. Journal version, to appear in Communications in Mathematical Physics |
| DOI: |
10.48550/arxiv.2105.00551 |
| URL الوصول: |
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d0d14fa49b8c5bc8ccddfa2db07dbf86 |
| Rights: |
OPEN |
| رقم الانضمام: |
edsair.doi.dedup.....d0d14fa49b8c5bc8ccddfa2db07dbf86 |
| قاعدة البيانات: |
OpenAIRE |