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Conformal fields, restriction properties, degenerate representations and SLE
Roland Friedrich, Wendelin Werner
In this note, we show how to relate the Schramm-Loewner Evolution processes (SLE) to highest-weight representations of the Virasoro Algebra. The conformal restriction properties of…
On the scaling limit of planar self-avoiding walk
Gregory F. Lawler, Oded Schramm, Wendelin Werner
A planar self-avoiding walk (SAW) is a nearest neighbor random walk path in the square lattice with no self-intersection. A planar self-avoiding polygon (SAP) is a loop with no sel…
One-arm exponent for critical 2D percolation
Gregory F. Lawler, Oded Schramm, Wendelin Werner
The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than is proved to decay like as .
Sharp estimates for Brownian non-intersection probabilities
Greg Lawler, Oded Schramm, Wendelin Werner
This paper gives an accessible (but still technical) self-contained proof to the fact that the intersection probabilities for planar Brownian motion are given in terms of the inter…
Critical exponents, conformal invariance and planar Brownian motion
Wendelin Werner
In this review paper, we first discuss some open problems related to two-dimensional self-avoiding paths and critical percolation. We then review some closely related results (join…
A counterexample to the "hot spots" conjecture
Krzysztof Burdzy, Wendelin Werner
We construct a counterexample to the ``hot spots'' conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in t…