کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10527286 958770 2012 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes
چکیده انگلیسی
Let L be a reversible Markovian generator on a finite set V. Relations between the spectral decomposition of L and subpartitions of the state space V into a given number of components which are optimal with respect to min-max or max-min Dirichlet connectivity criteria are investigated. Links are made with higher-order Cheeger inequalities and with a generic characterization of subpartitions given by the nodal domains of an eigenfunction. These considerations are applied to generators whose positive rates are supported by the edges of a discrete cycle ZN, to obtain a full description of their spectra and of the shapes of their eigenfunctions, as well as an interpretation of the spectrum through a double-covering construction. Also, we prove that for these generators, higher Cheeger inequalities hold, with a universal constant factor 48.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 122, Issue 4, April 2012, Pages 1748-1776
نویسندگان
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