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Scaling limit for the ant in a high-dimensional labyrinth.

It is believed that in high dimensions, a large critical percolation cluster should scale to the so-called integrated super Brownian excursion (ISBE). Moreover, it is also believed that a simple random walk in the critical percolation cluster should scale to the Brownian motion on the ISBE. In this talk I will present a result that gives conditions for a general sequence of random subgraphs of Z^d under which the random walk on these graphs scales to the Brownian motion on the ISBE. We will show how to apply this general theorem in the case where the graphs are obtained as the trace of critical branching random walks in Z^d, d>12. Joint work with Gerard Ben Arous and Alexander Fribergh