Random walk loop soup
By Gregory F. Lawler, J. A. T. Ferreras. 2004
108 citations recorded by the source corpus.
The Brownian loop soup introduced by Lawler and Werner (2004) is a Poissonian realization from a σ-finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Komlos, Major, and Tusnady. To make the paper self-contained, we include a proof of the approximation result that we need.
Subfields: Artificial Intelligence, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b1a95039f0ffb346b8030004be89066013e28276
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Wendelin Werner
- Michael J. Kozdron
- Julien Dubédat
- Scott Sheffield
- Gregory F. Lawler
- Oded Schramm
- Federico Camia
- Charles M. Newman
In Mathematical Physics
- Julien Dubédat
- Scott Sheffield
- Wendelin Werner
- Gregory F. Lawler
- Michael J. Kozdron
- Oded Schramm
- Jason Miller
- Vincent Beffara
Citations in the corpus
- SLE and the free field: partition functions and couplings (2007, background): “Most of the discussion here can be carried out at the level of Markov chains ([25, 27])”
- The configurational measure on mutually avoiding SLE paths (2006, methodology): “If we scale the loops by N and take the limit, we get the Brownian loop measure [13] as mentioned in Section 2.”
- Conformal loop ensembles: the Markovian characterization and the loop-soup construction (2010, background): “Sample of a random-walk loop-soup approximation [19] of a Brownian loop-soup in a square, by Serban Nacu.”