Abstract

I will continue the discussion on hitting probabilities and focus on the case of critical dimensions. Although the general bounds for hitting probabilities allow us to determine whether a fixed point is polar in non-critical dimensions, they are usually inconclusive in critical dimensions. I will present Talagrand’s covering argument, which can be used to prove that points are polar in critical dimensions for Gaussian random fields. If time permits, I will also talk about a recent result for solutions of nonlinear stochastic heat equations which are non-Gaussian random fields.