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...

We describe a method for identifying random walks. This method is based on the previously proposed small shuffle surrogate method. Hence, our method does not depend on the specific data distribution, although previously proposed methods depend on properties of the data distribution. The method is demonstrated for numerical data generated by known systems, and applied to several actual time seri...

Random walk simulation is employed in many experimental algorithmic applications. Efficient execution on modern computer architectures demands that the random walk be implemented to exploit data locality for improving the cache performance. In this research, we demonstrate how different one-dimensional data reordering functionals can be used as a preprocessing step for speeding the random walk ...

We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are very attractive alternative processes to classical cascade-like multifractal models since they do not involve any particular scale ratio. The MRWs are indexed b...

We study a discrete time self interacting random process on graphs, which we call Greedy Random Walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not been crossed yet by the walker. At each step, the walker being at some vertex, picks an adjacent edge among the edges that have not traversed thus far accor...