Abstract: Let fW be a two-parameter, Rd-valued generalized Brownian sheet. We can view fW as a sequence of interacting generalized Brownian motions or slices. The sample path properties for the slices of fW are studied, and the connections between the polar sets for the slices of fW and capacity are also presented. A common feature of our results is that exhibit phase transition.
DOI: *As the DOI is a unique identifier, it is already available in the pdf version. **The DOI link will be activated in the first midst of January 2026.