

Polymers can be considered random walks, if looked at on the appropriate
scale. We will exploit this quite heavily not only from an analytical point of view, but
also for computational methods. To give you an idea of what is involved lets make small
detour: We assume a lattice. For simplicity we take a simple square lattice. On this
lattice a particle or walker is placed. The walker regards this initial position as the
origin. The walker draws a random number and decides, according to the drawn random
number, to go to a new position on the lattice. The new position must be one of the
nearest neighbors and each of the neighbors has the same probability to be visited. Once
he is at the new position, the walker regards this position as his new origin. In other
words, he immediately forgets where he came from. Every step is made as if it is the first
step. All steps are then independent of each other. Schematically a walk is shown in the
following picture. 