Harness processes and harmonic crystals

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:116

Article

Ferrari, Pablo A. ; Niederhauser, Beat M.

关键词: harness process;    linear Gaussian processes;    surface dynamics;   

DOI  :  10.1016/j.spa.2005.12.004

来源: Elsevier

【 摘 要 】

In the Hammersley harness processes the R-valued height at each site i is an element of Z(d) is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process a la Harris simultaneously for all times and boxes contained in Zd. With this representation we compute covariances and show L-2 and almost sure time and space convergence of the process. In particular, the process started from the flat configuration and viewed from the height at the origin converges to an invariant measure. In dimension three and higher, the process itself converges to an invariant measure in L-2 at speed t(1-d/2) (this extends the convergence established by Hsiao). When the noise is Gaussian the limiting measures are Gaussian fields (harmonic crystals) and are also reversible for the process. (C) 2006 Published by Elsevier B.V.

【 授权许可】

Free