scholarly journals UST branches, martingales, and multiple SLE(2)

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Alex Karrila
Keyword(s):  
Multiple Sle

scholarly journals Schramm’s Formula and the Green’s Function for Multiple SLE

2019 ◽  
Vol 176 (4) ◽  
pp. 873-931 ◽  
Author(s):  
Jonatan Lenells ◽  
Fredrik Viklund
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Multiple Sle

scholarly journals Hydrodynamic Limit of Multiple SLE

2018 ◽  
Vol 171 (1) ◽  
pp. 166-188 ◽  
Author(s):  
Ikkei Hotta ◽  
Makoto Katori
Keyword(s):  
Hydrodynamic Limit ◽  
Multiple Sle

Multiple SLE and the complex Burgers equation

2016 ◽  
Vol 289 (16) ◽  
pp. 2007-2018 ◽  
Author(s):  
Andrea del Monaco ◽  
Sebastian Schleißinger
Keyword(s):  
Burgers Equation ◽  
Complex Burgers Equation ◽  
Multiple Sle

scholarly journals VIRASORO MODULE STRUCTURE OF LOCAL MARTINGALES OF SLE VARIANTS

2007 ◽  
Vol 19 (05) ◽  
pp. 455-509 ◽  
Author(s):  
KALLE KYTÖLÄ
Keyword(s):  
Generating Function ◽  
Coulomb Gas ◽  
Module Structure ◽  
Multiple Sle ◽  
Straightforward Approach

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 [Formula: see text] 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 [Formula: see text] 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.

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