Autocorrelation via renormalization (part I)
speaker: Franz Gähler (Faculty of Mathematics, Bielefeld University)abstract: The spectral properties of an aperiodic tiling generated by a primitive inflation rule are intimately related to its pair correlation functions. Thanks to the inflation symmetry, the latter satisfy a set of exact renormalisation relations, which relate correlation functions at large distances to their values at shorter distances. There is in fact a closed, finite system of consistency equations determining the short-distance correlations, whereas all other correlations are then determined purely recursively by these. The dimension of the solution space of short-distance correlations determines the number of independent correlation functions, and thus gives information on the spectral purity of the tiling. We illustrate the general theory and the different phenomena that occur with a number of well-know examples from the literature.
timetable:
Tue 5 Apr, 16:30 - 17:10, Aula Dini
<< Go back