کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904840 | 1633758 | 2018 | 99 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Full extremal process, cluster law and freezing for the two-dimensional discrete Gaussian Free Field
ترجمه فارسی عنوان
فرآیند کامل افراطی، قانون خوشه ای و انجماد برای میدان رایگان گاوسی گسسته دو بعدی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
We study the local structure of the extremal process associated with the Discrete Gaussian Free Field (DGFF) in scaled-up (square-)lattice versions of bounded open planar domains subject to mild regularity conditions on the boundary. We prove that, in the scaling limit, this process tends to a Cox process decorated by independent, correlated clusters whose distribution is completely characterized. As an application, we control the scaling limit of the discrete supercritical Liouville measure, extract a Poisson-Dirichlet statistics for the limit of the Gibbs measure associated with the DGFF and establish the “freezing phenomenon” conjectured to occur in the “glassy” phase. In addition, we prove a local limit theorem for the position and value of the absolute maximum. The proofs are based on a concentric, finite-range decomposition of the DGFF and entropic-repulsion arguments for an associated random walk. Although we naturally build on our earlier work on this problem, the methods developed here are largely independent.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 330, 25 May 2018, Pages 589-687
Journal: Advances in Mathematics - Volume 330, 25 May 2018, Pages 589-687
نویسندگان
Marek Biskup, Oren Louidor,