کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10527246 | 958744 | 2014 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Loop-erased random walk on the Sierpinski gasket
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
In this paper the loop-erased random walk on the finite pre-SierpiÅski gasket is studied. It is proved that the scaling limit exists and is a continuous process. It is also shown that the path of the limiting process is almost surely self-avoiding, while having Hausdorff dimension strictly greater than 1. The loop-erasing procedure proposed in this paper is formulated by erasing loops, in a sense, in descending order of size. It enables us to obtain exact recursion relations, making direct use of 'self-similarity' of a fractal structure, instead of the relation to the uniform spanning tree. This procedure is proved to be equivalent to the standard procedure of chronological loop-erasure.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 124, Issue 1, January 2014, Pages 566-585
Journal: Stochastic Processes and their Applications - Volume 124, Issue 1, January 2014, Pages 566-585
نویسندگان
Kumiko Hattori, Michiaki Mizuno,