## Wolfgang Woess

Math Colloquium

### Speaker: Wolfgang Woess, TU Graz

### Title: THE LANGUAGE OF SELF-AVOIDING WALKS

Location: VR-II, V-155

Time: Tuesday June 4 at 11.00 am

### Abstract:

Let X = (VX, EX) be an infinite, locally finite, connected graph without

loops or multiple edges. We consider the edges to be oriented, and EX is equipped with

an involution which inverts the orientation. Each oriented edge is labelled by an element

of a finite alphabet Σ. The labelling is assumed to be deterministic: edges with the same

initial (resp. terminal) vertex have distinct labels. Furthermore it is assumed that the

group of label-preserving automorphisms of X acts quasi-transitively. For any vertex o

of X, consider the language of all words over Σ which can be read along self-avoiding

walks starting at o. We characterize under which conditions on the graph structure this

language is regular or context-free. This is the case if and only if the graph has more

than one end, and the size of all ends is 1, or at most 2, respectively. (joint work with Christian Lindorfer).