Abstract
By a well known calculation on Gaussian measure, if X is finite, for any \({X}{\varepsilon}{\mathbb{R}}^{X}_{+}\) \(\frac{\sqrt{\det(M_{\lambda}-C)}}{(2\pi)^{\left| X\right| /2}}\int_{\mathbb{R}^{X}}e^{-\frac{1}{2}\sum\chi_{u}(v^{u})^{2}}e^{-\frac{1} {2}e(v)}\Pi_{u\in X}dv^{u}=\sqrt{\frac{\det(G_{\chi})}{\det(G)}}\) and \(\frac{\sqrt{\det(M_{\lambda}-C)}}{(2\pi)^{\left| X\right| /2}}\int_{\mathbb{R}^{X}}v^xv^ye^{-\frac{1}{2}\sum\chi_{u}(v^{u})^{2}}e^{-\frac{1} {2}e(v)}\Pi_{u\in X}dv^{u}=(G_{\chi})^{x,y}\sqrt{\frac{\det(G_{\chi})}{\det(G)}} \)
Keywords
- Integrable Functional
- Dirichlet Space
- Wick Product
- Symmetric Tensor Product
- Intersection Local Time
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Jan, Y.L. (2011). The Gaussian Free Field. In: Markov Paths, Loops and Fields. Lecture Notes in Mathematics(), vol 2026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21216-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-21216-1_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21215-4
Online ISBN: 978-3-642-21216-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
