Abstract
Recall that an oriented link g is a pair of points \((g^{-},g^{+})\,{\rm {such that}} \,C_{g}=C_{g^{-},g^{+}}\neq0\,. {\rm{Define}} \,-g=(g^{+},g^{-})\,.\,{\rm{Let} \,\mu_{\neq}^{x,y}\,{\rm{ be\, the\, measure\, induced\, by\, C\, on\, discrete\, self-avoiding\, paths\, between\, x\, and\, y\,}}: \,\mu_{\neq}^{x,y}(x,x_{2},...,x_{n-1}\,,y)=C_{x,x_{2}}C_{x_{1},x_{3}}... C_{x_{n-1},y}}.\)
Another way to define a measure on discrete self avoiding paths from x to y from a measure on paths from x to y is loop erasure defined in Sect. 3.1 (see also [16, 17, 39] and [31]). In this context, the loops, which can be reduced to points, include holding times, and loop erasure produces a discrete path without holding times.
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). Loop Erasure and Spanning Trees. 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_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-21216-1_8
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)
