| | |
| | |
Stat |
Members: 3645 Articles: 2'501'711 Articles rated: 2609
20 April 2024 |
|
| | | |
|
Article overview
| |
|
Finite range Decomposition of Gaussian Processes | David C.Brydges
; G.Guadagni
; P.K.Mitter
; | Date: |
5 Mar 2003 | Subject: | Mathematical Physics; Statistical Mechanics MSC-class: 81T08;81T17;81T25;60G15;60G52;60G18 | math-ph cond-mat.stat-mech hep-lat hep-th math.MP | Affiliation: | University of British Columbia), G.Guadagni (University of Virginia), P.K.Mitter (Universite Montpellier 2 | Abstract: | Let $D$ be the finite difference Laplacian associated to the lattice $Z^{d}$. For dimension $dge 3$, $age 0$ and $L$ a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent $G^{a}:=(a-D)^{-1}$ can be decomposed as an infinite sum of positive semi-definite functions $ V_{n} $ of finite range, $ V_{n} (x-y) = 0$ for $|x-y|ge O(L)^{n}$. Equivalently, the Gaussian process on the lattice with covariance $G^{a}$ admits a decomposition into independent Gaussian processes with finite range covariances. For $a=0$, $ V_{n} $ has a limiting scaling form $L^{-n(d-2)}Gamma_{c,ast}{igl (frac{x-y}{L^{n}}igr)}$ as $n o infty$. As a corollary, such decompositions also exist for fractional powers $(-D)^{-alpha/2}$, $0 | Source: | arXiv, math-ph/0303013 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |