Dimitry Beliaev: Factorization formulas for percolation

We compute the probability that one interior and one boundary point are close to the percolation cluster which is attached to a boundary interval. In general, these high order correlation functions are extremely difficult to analise, but in this particular case it turened out to be possible to find an exact answer. Moreover, one can show that probabilities of several events of this type can be expressed in terms of probabilities of much simplier events.