Papers+of+General+Interest+to+all+Program+Participants

Feel free to add links to any material on the web which you think might interest people in this program.

Reviews of SLE:
1. [|Conformally invariant scaling limits (an overview and a collection of problems)] - Oded Schramm. 2. [|SLE for theoretical physicists] - John Cardy. 3. [|A Guide to Stochastic Loewner Evolution and its Applications]- Wouter Kager, Bernard Nienhuis. 4. [|Critical exponents, conformal invariance and planar Brownian motion] - Wendelin Werner. 5. [|Some recent aspects of random conformally invariant systems] - Wendelin Werner. 6. [|Conformal restriction and related questions] - Wendelin Werner. 7. [|Gaussian free fields for mathematicians] - Scott Sheffield. 8. [|2D growth processes: SLE and Loewner chains -] Michel Bauer, Denis Bernard

Reviews written by and for mathematicians G. F. Lawler, Conformally invariant processes in the plane. Mathematical Surveys and Monographs, 114. American Mathematical Society, Providence, RI, 2005.

G. F. Lawler, Conformally invariant processes in the plane, available online at URL http://www.math.cornell.edu/~lawler/papers.htmlG. F. Lawler, Conformal invariance, universality, and the dimension of the Brownian frontier, Proceedings of the International Congress of Mathematicians, Vol. III, 63--72 (Higher Ed. Press, Beijing, 2002); arXiv: math.PR/0304369.

G. F. Lawler, An introduction to the stochastic Loewner evolution, Random walks and geometry, 261--293, Walter de Gruyter GmbH \& Co. KG (Berlin 2004); available online at URL http://www.math.cornell.edu/~lawler/papers.htmlG. F. Lawler, Stochastic Loewner evolution, a draft of a contribution on SLE to Encyclopedia of Mathematical Physics to be published by Elsevier, available online at URL http://www.math.cornell.edu/~lawler/papers.html

O. Schramm, Scaling limits of random processes and the outer boundary of planar Brownian motion, Current developments in mathematics, 2000, 233--253 (Int. Press, Somerville, MA, 2001).

O. Schramm, Emergence of symmetry: conformal invariance in scaling limits of random systems, European Congress of Mathematics, 783--786, Eur. Math. Soc., Z\"urich, 2005.

O. Schramm, Conformally invariant scaling limits (an overview and a collection of problems), to appear in the ICM 2006 Madrid Proceedings, arXiv: math.PR/0602151.

S. Sheffield, Gaussian free fields for mathematicians, arXiv: math.PR/0312099.

W. Werner, Critical exponents, conformal invariance and planar Brownian motion, European Congress of Mathematics, Vol. II (Barcelona, 2000), 87--103, Progr. Math., 202, Birkhauser, Basel, 2001; arXiv: math.PR/0007042.

W. Werner, Random planar curves and Schramm-Loewner evolutions, Lectures on probability theory and statistics. Lectures from the 32nd Probability Summer School held in Saint-Flour, July 7--24, 2002. Lecture Notes in Mathematics, 1840. Springer-Verlag (Berlin, 2004); arXiv: math.PR/0303354.

W. Werner, Conformal restriction and related questions, Prob. Surveys 2, 145--190 (2005); arXiv: math.PR/0307353.

W. Werner, Some recent aspects of random conformally invariant systems, arXiv: math.PR/0511268.


 * Reviews written by and for physicists**
 * Reviews written by and for physicists**

M. Bauer and D. Bernard, Loewner chains, in String theory: from gauge interactions to cosmology, 41--77, NATO Sci. Ser. II Math. Phys. Chem., 208, Springer, Dordrecht, (2006); arXiv: cond-mat/0412372.

M. Bauer and D. Bernard, 2D growth processes: SLE and Loewner chains, arXiv: math-ph/0602049.

J. Cardy, Conformal invariance in percolation, self-avoiding walks and related problems, arXiv: cond-mat/0209638.

J. Cardy, SLE for theoretical physicists, Ann. Phys. 318, 81--118 (2005); arXiv: cond-mat/0503313.

B. Duplantier, Conformal fractal geometry and boundary quantum gravity, in Fractal geometry and applications: a jubilee of Benoît Mandelbrot, Part 2, 365--482, Proc. Sympos. Pure Math., 72, Part 2, AMS, 2004; arXiv: math-ph/0303034.

I. A. Gruzberg, Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory, arXiv: math-ph/0607046.

I. A. Gruzberg and L. P. Kadanoff, The Loewner equation: maps and shapes, J. Stat. Phys. 114, 1183--1198 (2004); arXiv: cond-mat/0309292.

W. Kager, B. Nienhuis, A Guide to Stochastic Loewner Evolution and its Applications, J. Stat. Phys. 115, 1149--1229 (2004); arXiv: math-ph/0312056.