Sharp Asymptotics for Arm Probabilities in Critical Planar Percolation

In this work, we consider critical planar site percolation on the triangular lattice and derive sharp estimates on the asymptotics of the probability of half-plane j-arm events for \(j\ge 1\) $j\ge 1$ and planar (polychromatic) j-arm events for \(j>1\) $j>1$ , building upon a recent, not yet peer-reviewed result of Binder and Richards (Convergence rates of random discrete model curves approaching sle curves in the scaling limit. Preprint, 2020). These estimates greatly improve previous results and in particular answer (a large part of) a question of Schramm (ICM Proc., 2006).