We start our lectures with introducing and discussing the general notion of multifractality spectrum for random measures on lattices, and how it can be probed using moments of that measure. Then we show that the Boltzmann–Gibbs probability distributions generated by logarithmically correlated...

We compute the second order correction for the cover time of the binary tree of depth n by (continuous-time) random walk, and show that with probability approaching 1 as n increases, τcov=|E|[2log2⋅n−logn/2log2+O((loglogn)8)], thus showing that the second order correction differs from the...

We consider continuous-time random interlacements on Zd, d≥3, and investigate the percolation model where a site x of Zd is occupied if the total amount of time spent at x by all the trajectories of the interlacement at level u≥0 exceeds some constant α≥0, and empty otherwise. We also...

We consider creep processes in plastically deformed materials as a critical process such as proposed by Zaitsev (Physica A 189 (1992) 411). We give arguments that the low-temperature creep rate necessarily has two different modes. During the first (fast) stage of stress relaxation, dislocations...

We study the motion of a massive particle in a quenched random environment at zero temperature. The distribution of particle positions is investigated numerically and special focus is placed on the mean stopping distance and its fluctuations. We apply a scaling analysis in order to obtain...