We show that under a 3+[delta] moment condition (where [delta]0) there exists a 'Hartman-Winter' Law of the iterated logarithm for random walks conditioned to stay non-negative. We also show that under a second moment assumption the conditioned random walk eventually grows faster than n1/2(log...

We consider the hydrodynamic limit for a certain Brownian directed percolation model, and establish uniform concentration results. In view of recent work on the connection between this directed percolation model and eigenvalues of random matrices, our results can also be interpreted as uniform...

We discuss the homogenization problem for a particular class of nested fractals, called "tree-like" Vicsek sets, which are not covered by the class considered in Kumagai and Kusuoka (1996). Random irreducible conductivities are assigned to each cell in the infinite fractal lattice and then we...

We consider a class of random recursive Sierpinski gaskets and examine the short-time asymptotics of the on-diagonal transition density for a natural Brownian motion. In contrast to the case of divergence form operators in or regular fractals we show that there are unbounded fluctuations in the...