Metastability and small eigenvalues in Markov chains

被引:18
作者
Bovier, A
Eckhoff, M
Gayrard, V
Klein, M
机构
[1] Weierstrass Inst Angew Anal & Stochast, D-10117 Berlin, Germany
[2] Univ Potsdam, Inst Math, D-14469 Potsdam, Germany
[3] CNRS, Ctr Phys Theor, F-13288 Marseille, France
[4] EPFL, DMA, CH-1021 Lausanne, Switzerland
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2000年 / 33卷 / 46期
关键词
D O I
10.1088/0305-4470/33/46/102
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this Letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerably greater precision than has so far been available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state and sharp estimates of the convergence of the probability distribution of the metastable transition times to the exponential distribution.
引用
收藏
页码:L447 / L451
页数:5
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