We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
VIRASORO MODULE STRUCTURE OF LOCAL MARTINGALES OF SLE VARIANTS.
- Authors
KYTÖLÄ, KALLE
- Abstract
Martingales often play an important role in computations with Schramm–Loewner Evolutions (SLEs). The purpose of this article is to provide a straightforward approach to the Virasoro module structure of the space of local martingales for variants of SLEs. In the case of ordinary chordal SLE, it has been shown in Bauer and Bernard's Phys. Lett. B557 that polynomial local martingales form a Virasoro module. We will show for more general variants that the module of local martingales has a natural submodule $\mathcal{M}$ that has the same interpretation as the module of polynomial local martingales of chordal SLE, but it is in many cases easy to find more local martingales than that. We discuss the surprisingly rich structure of the Virasoro module $\mathcal{M}$ and construction of the "SLE state" or "martingale generating function" by Coulomb gas formalism. In addition, Coulomb gas or Feigin–Fuchs integrals will be shown to transparently produce candidates for multiple SLE pure geometries.
- Subjects
MARTINGALES (Mathematics); COULOMB functions; STOCHASTIC processes; PROBABILITY theory; MATHEMATICAL combinations
- Publication
Reviews in Mathematical Physics, 2007, Vol 19, Issue 5, p455
- ISSN
0129-055X
- Publication type
Article