A correction to this paper has been published: 10.1007/s00440-016-0699-z

Let Xk, k= 1, 2, 3, • • -, be a sequence of mutually independent random variables on an appropriate probability space which have a given common distribution function F. Let Sn = Xi+ • • • +Xn, then the event lim inf | S„\ = 0 has probability either zero or one. If this event has zero chance, we say F is transient; in the other case, | 5„| tends to infinity almost surely, and F is called recurre...

– The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using the method of moments. When the number of iterations n → ∞, a time-independent asymptotic density is obtained. It has a simple symmetric exponential form ...

We consider the random walk attachment graph introduced by Saramäki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential attachment may appear requiring only local knowledge. We show that if the length of the random walk is fixed then the resulting graphs can have properties significantly different from those of preferential attachment graphs, and in particular...

There are a large number of different modifications and variants of the usual symmetrical random walk ~RW!. Let us mention only Levy flights, biased diffusions, self-avoiding walk ~SAW for short!, etc. Let us confine ourselves to the random walks on the discrete lattices. In SAW a walking particle is choosing its trajectory in such a way that it does not step down onto the already visited site....

A random walk on Z is excited if the first time it visits a vertex there is a bias in one direction, but on subsequent visits to that vertex the walker picks a neighbor uniformly at random. We show that excited random walk on Z is transient iff d > 1. 1. Excited Random Walk A random walk on Z is excited (with bias ε/d) if the first time it visits a vertex it steps right with probability (1 + ε)...

Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media, composite materials and biological tissues. A major challenge is to characterize the microstructure of a material or an organism nondestructively using a bulk transport measurement. Here we demonstrate how the long-range structural correlations introduced by permeable membranes give rise to distinct feature...