### Recent Papers Gregory F. Lawler

Here are some references to recent papers, preprints, and drafts. For references to older papers you may check my vita. My research is partially supported by the National Science Foundation.

For some _rough_ drafts of some other material you can check in progress.

This is a draft of Uniform spanning forests and the bi-Laplacian Gaussian field (with X. Sun and W. Wu)

Convergence of loop-erased random walk in the natural parametrization (with F. Viklund)

Compressed self-avoiding walks, bridges and polygons (with N. Beaton, A. Guttmann, and I. Jensen)

Up-to-constants bounds on the two-point Green's function for SLE curves (with M. Rezaei)

Minkowski content of the intersection of a Schramm-Loewner evolution (SLE) curve with the real line to appear in a volume in memory of Kiyoshi Ito.

Escape probability and transience for SLE
(with L. Field) (with J. Perlman) This is an introduction to discrete loop measures to be submitted to the proceedings of the 2013 Prague summer school in statistical mechanics.

Scaling limit of the loop-erased random walk Green's function
(with C. Benes and F. Viklund)

Random walk problems motivated by statistical physics . This is an extended version of a talk I gave at the St. Petersburg summer school in Probability and Statistical Physics in 2012. (with M. Alvisio) (with M. Rezaei) (with L. Field) (with T. Alberts and M. Kozdron) (with M. Rezaei) (with T. Kennedy) These are a combination of my notes from summer school courses at University of Washington (2010) and Cornell University (2011) (updated April, 2011) (with B. Werness) (with B. Dyhr, M. Gilbert, T. Kennedy, S. Passon) (with B. Vermesi) These are notes from my lectures at the 2010 Clay Mathematics Institute school in Buzios, Brazil (Revised, Dec, 2010) (with W. Zhou) (with F. Johansson) (with S. Lalley and H. Narayanan) (with F. Johansson) This paper is based on the preprint "Dimension and natural parametrization for SLE'' that was never published. (Some of the material in the latter preprint went into the paper with S. Sheffield). The final version appears in Fractal Geometry Stochastics IV published by Birkh\"auser. (with S. Sheffield). This paper establishes the existence of the natural parametrization for some values of kappa (updated June 22, 2009) This is an informal paper discussing the correct definition of annulus'' and radial from an interior point'' so that one expects reversibility to hold. There are more open questions than results in this paper. The final version appears in Journal of Statistical Physics. (with H. Narayanan)