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...

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...