کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5772469 1413371 2017 72 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Long time asymptotics of non-symmetric random walks on crystal lattices
ترجمه فارسی عنوان
ضریب همبستگی طولانی در حالت تصادفی غیر متقارن بر روی شبکه های کریستالی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
In the present paper, we study long time asymptotics of non-symmetric random walks on crystal lattices from a view point of discrete geometric analysis due to Kotani and Sunada [11,25]. We observe that the Euclidean metric associated with the standard realization of the crystal lattice, called the Albanese metric, naturally appears in the asymptotics. In the former half of the present paper, we establish two kinds of (functional) central limit theorems for random walks. We first show that the Brownian motion on the Euclidean space with the Albanese metric appears as the scaling limit of the usual central limit theorem for the random walk. Next we introduce a family of random walks which interpolates between the original non-symmetric random walk and the symmetrized one. We then capture the Brownian motion with a constant drift of the asymptotic direction on the Euclidean space with the Albanese metric associated with the symmetrized random walk through another kind of central limit theorem for the family of random walks. In the latter half of the present paper, we give a spectral geometric proof of the asymptotic expansion of the n-step transition probability for the non-symmetric random walk. This asymptotic expansion is a refinement of the local central limit theorem obtained by Sunada [22,23] and is a generalization of the result in [11] for symmetric random walks on crystal lattices to non-symmetric cases.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 272, Issue 4, 15 February 2017, Pages 1553-1624
نویسندگان
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