کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4589859 | 1334915 | 2015 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A uniqueness result for minimizers of the 1D Log-gas renormalized energy
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In [21] Sandier and Serfaty studied the one-dimensional Log-gas model, in particular they gave a crystallization result by showing that the one-dimensional lattice Z is a minimizer for the so-called renormalized energy which they obtained as a limit of the N-particle Log-gas Hamiltonian for Nââ. However, this minimizer is not unique among infinite point configurations (for example local perturbations of Z leave the renormalized energy unchanged). In this paper, we establish that uniqueness holds at the level of (stationary) point processes, the only minimizer being given by averaging Z over a choice of the origin in [0,1]. This is proved by showing a quantitative estimate on the two-point correlation function of a process in terms of its renormalized energy.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 268, Issue 7, 1 April 2015, Pages 1649-1677
Journal: Journal of Functional Analysis - Volume 268, Issue 7, 1 April 2015, Pages 1649-1677
نویسندگان
Thomas Leblé,