English

Schramm's formula and the Green's function for multiple SLE

Probability 2019-06-12 v3 Mathematical Physics math.MP

Abstract

We construct martingale observables for systems of multiple SLE curves by applying screening techniques within the CFT framework recently developed by Kang and Makarov, extended to admit multiple SLEs. We illustrate this approach by rigorously establishing explicit expressions for the Green's function and Schramm's formula in the case of two curves growing towards infinity. In the special case when the curves are `fused' and start at the same point, some of the formulas we prove were predicted in the physics literature.

Cite

@article{arxiv.1701.03698,
  title  = {Schramm's formula and the Green's function for multiple SLE},
  author = {Jonatan Lenells and Fredrik Viklund},
  journal= {arXiv preprint arXiv:1701.03698},
  year   = {2019}
}

Comments

54 pages

R2 v1 2026-06-22T17:49:39.184Z