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. Included there are working chapters on my book project on SLE and related mathematics.

Transition probabilities for infinite two-sided loop-erased random walks (with C. Benes and F. Viklund)

This is a draft of Notes on the Bessel process. This is an introduction to the Bessel process motivated by applications to SLE.

Conformally invariant loop measures Proceedings 2018 ICM.

Weighted graphs and complex Gaussian fields (with P. Panov)

Minkowski content of Brownian cut points (with N. Holden, X. Li, and X. Sun)

The infinite two-sided loop-erased random walk

On the smoothness of the partition function for multiple Schramm-Loewner evolutions (with M. Jahangoshahi)

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

The Loewner difference equation and the convergence of loop-erased random walk (with F. Viklund)

This is a draft of A note on the boundary exponent and rate of escape for the Schramm-Loewner evolution (with B. Werness)

Topics in loop measures and loop-erased random walk These are notes from a course given in Fall, 2016 at the University of Chicago.

Loop-erased random walk, uniform spanning forests and bi-Laplacian Gaussian field in the critical dimension (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)

Loop measures and the Gaussian free 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.

Note on the existence and modulus of continuity of the SLE_8 curve
(with M. Alvisio)

The probability that planar loop-erased random walk uses a given edge

Minkowski content and natural parameterization for the Schramm-Loewner evolution
(with M. Rezaei)

Reversed radial SLE and the Brownian loop measure
(with L. Field)

The Green's function for the radial Schramm-Loewner evolution
(with T. Alberts and M. Kozdron)

Basic properties of the natural parametrization for the Schramm-Loewner evolution
(with M. Rezaei)

Lattice effects in the scaling limit of the two-dimensional self-avoiding walk
(with T. Kennedy)

Defining SLE in multiply connected domains with the Brownian loop measure

Comments on Edward Nelson's ``Internal set theory: A new approach to nonstandard analysis''

Scaling limits and SLE
These are a combination of my notes from summer school courses at University of Washington (2010) and Cornell University (2011)

Continuity of radial and two-sided radial SLE_\kappa at the terminal point
(updated April, 2011)

Multi-point Green's Functions for SLE and an estimate of Beffara
(with B. Werness)

The self-avoiding walk in a strip
(with B. Dyhr, M. Gilbert, T. Kennedy, S. Passon)

Fast convergence to an invariant measure for non-intersection 3-dimensional Brownian paths
(with B. Vermesi)

Fractal and multifractal properites of SLE
These are notes from my lectures at the 2010 Clay Mathematics Institute school in Buzios, Brazil (Revised, Dec, 2010)

SLE curves and natural parametrization
(with W. Zhou)

Almost sure multifractal spectrum for the tip of an SLE curve
(with F. Johansson)

A geometric interpretation of half-plane capacity
(with S. Lalley and H. Narayanan)

Optimal Holder exponent for the SLE path
(with F. Johansson)

Mulltifractal analysis of the reverse flow for the Schramm-Lowener evolution
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.

The natural parametrization for the Schramm-Loewner evolution
(with S. Sheffield). This paper establishes the existence of the natural parametrization for some values of kappa (updated June 22, 2009)

Partition functions, loop measures, and versions of SLE
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.

Mixing times and $l_p$ bounds for oblivous routing
(with H. Narayanan)