Mixing time and eigenvalues of the abelian sandpile Markov chain
نویسندگان
چکیده
منابع مشابه
Eigenvalues and Mixing Time
Mixing time of a Markov chain depends on the eigenvalues of its transition matrix. We give some examples and bounds on the mixing time in terms of the eigenvalue having second largest absolute value. This paper is based on Chapters 1, 4, and 12 of [1].
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The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice Zd, in which sites with at least 2d chips topple, distributing 1 chip to each of their neighbors in the lattice, until no more topplings are possible. From an initial configuration consisting of n chips placed at a single vertex, the rescaled stable configuration seems ...
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The Abelian sandpile model is the simplest analytically tractable model of self-organized criticality. This paper presents a brief review of known results about the model. The abelian group structure of the algebra of operators allows an exact calculation of many of its properties. In particular, when there is a preferred direction, one can calculate all the critical exponents characterizing th...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2019
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7585