Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

FOCS

2006

IEEE

2006

IEEE

Spin systems are a general way to describe local interactions between nodes in a graph. In statistical mechanics, spin systems are often used as a model for physical systems. In computer science, they comprise an important class of families of combinatorial objects, for which approximate counting and sampling algorithms remain an elusive goal. The Dobrushin condition states that every row sum of the “inﬂuence matrix” for a spin system is less than 1 − ε, where ε > 0. This criterion implies rapid convergence (O(n log n) mixing time) of the single-site (Glauber) dynamics for a spin system, as well as uniqueness of the Gibbs measure. The dual criterion that every column sum of the inﬂuence matrix is less than 1 − ε has also been shown to imply the same conclusions. We examine a common generalization of these conditions, namely that the maximum eigenvalue of the inﬂuence matrix is less than 1 − ε. Our main result is that this criterion implies O(n log n) mixing time...

Added |
11 Jun 2010 |

Updated |
11 Jun 2010 |

Type |
Conference |

Year |
2006 |

Where |
FOCS |

Authors |
Thomas P. Hayes |

Comments (0)