5 problems

Let the incipient infinite cluster (IIC) be the random configuration obtained as the local limit of critical percolation conditioned on the origin being connected to distance tendi…

Cardy's formula. The scaling limit exists and equals the conformal coordinate of $X$:

The range of branching random walk and critical lattice trees are simpler models whose random-walk scaling limits have been studied. They are conjectured to belong to the same univ…

The constants $K_3$, $K_4$, and $K_5$ are non-universal normalization-dependent constants arising from the definitions of point neighborhoods, whereas $K_F$ is the constant in the…

Super-strong separation lemma. Conditioned on at least four of these interfaces reaching $B(R_1)$, the set of interfaces reaching $R_1$ has positive quality with positive probabili…