Conformally Invariant Processes in the Plane

By Gregory F. Lawler. 2005

774 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/3c5bddf01145fce7d00ead2908105c38c187693d

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Citations in the corpus

Towards conformal invariance of 2D lattice models (2007, methodology): “We will omit the precise definition of allowed slits (more extensive discussion in this context can be found in [22]), only noting that all simple curves are included.”
Critical percolation exploration path and SLE6: a proof of convergence (2006, methodology): “Here we describe the chordal version of SLEκ; for more, see [27] as well as the fine reviews by Lawler [18], Kager and Nienhuis [15], and Werner [37], and Lawler’s book [ 19 ].”
SLE for theoretical physicists (2005, background): “riginal papers on SLE are mostly both long and diﬃcult, using, moreover, concepts and methods foreign to most theoretical physicists. There are reviews, in particular those by Werner[12] and by Lawler[13] which cover much of the important material in the original papers. These are however written fo”
Quantitative noise sensitivity and exceptional times for percolation (2005, background): “Proposition A16 in Lawler [22] indicates this general type of argument.”
Duality of chordal SLE (2007, background): “For basic properties of SLE, see [6] and [11].”
SLE and the free field: partition functions and couplings (2007, neutral): “For general background on SLE, see [31, 40, 23].”
Optimal Holder exponent for the SLE path (2009, methodology): “stant c 2 such that by iterating (8) along the path at most c 2(logr+1) times |f′(z)| ≤ cc2(logr+1) 1 |f ′(w)| = crα|f′(w)|, for α= c 2 logc 1 and c= cc2 1 . A proof of the next lemma may be found in [Law05]. For a set K, we let diam(K) denotes the diameter of Kand height(K) := sup{Im z: z∈ K}. Lemm”
Euler Integrals for Commuting SLEs (2005, neutral): “For general background on SLE, see [23, 28, 18].”
Convergence of Ising interfaces to Schramm's SLE curves (2013, methodology): “Schramm showed that those are the only possible conformally invariant scaling limits of interfaces in 2D critical lattice models, and the convergence to SLE was indeed proved in a number of cases, see [13, 17].”