We consider critical oriented Bernoulli percolation on the square lattice \mathbb{Z}^2. We prove a Russo-Seymour-Welsh type result which allows us to derive several new results concerning the critical behavior:
- We establish that the probability that the origin is connected to distance n decays polynomially fast in n.
- We prove that the critical cluster of the origin conditioned to survive to distance n has a typical width w_n satisfying \epsilon n^{2/5} < w_n < n^{1-\epsilon} for some \epsilon > 0. The sub-linear polynomial fluctuations contrast with the supercritical regime where w_n is known to behave linearly in n. It is also different from the critical picture obtained for non-oriented Bernoulli percolation, in which the scaling limit is non-degenerate in both directions. All our results extend to the graphical representation of the one-dimensional contact process.
