Boundary correlations in planar LERW and UST
Student No.:50
Time:Fri 10:00-11:00, 2017-08-25
Instructor:Eveliina Peltola  
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-8-25
Ending Date:2017-8-25





We study boundary visit events for loop-erased random walks (LERW) and connectivity events for branches in the uniform spanning tree (UST). By finding explicit formulas for them, we show that (when suitably renormalized), these probabilities converge in the scaling limit to conformally covariant functions, which satisfy partial differential equations of second and third order, as predicted by conformal field theory (CFT). These functions can be related to CFT correlation functions (with kappa=2): that is, pure partition functions of multiple SLEs, SLE Green functions, and conformal blocks of CFT. A similar structure seems to remain for general kappa as well. The talk is based on joint work with Alex Karrila and Kalle Kytölä (Aalto University).