Name
Abstract | ||
|---|---|---|
We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm or the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is 0 (as in heat bath dynamics). We apply the matrix norm methods to random update and systematic scan Glauber dynamics for coloring various classes of graphs. We give a general method for estimating a norm of asymmetric nonregular matrix. This leads to improved mixing times for any class of graphs which is hereditary and sufficiently sparse including several classes of degree-bounded graphs such as nonregular graphs, trees, planar graphs and graphs with given tree-width and genus. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1214/08-AAP532 | ANNALS OF APPLIED PROBABILITY |
Keywords | Field | DocType |
Matrix norms, rapid mixing, Markov chains, spin systems | Diagonal,Discrete mathematics,Glauber,Matrix (mathematics),Matrix function,Symmetric matrix,Matrix norm,Band matrix,Planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
19 | 1 | 1050-5164 |
Citations | PageRank | References |
11 | 0.80 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Martin E. Dyer | 1 | 529 | 116.66 |
| leslie ann goldberg | 2 | 1411 | 125.20 |
| mark jerrum | 3 | 2755 | 564.62 |