On the diffraction of constant shape random substitutions

Final Defense
On the diffraction of constant shape random substitutions

by Jim Ralphealo R. Mijares
MS Mathematics Candidate

Date: Thursday, 20 June 2024
Time: 4 pm
Venue: Hybrid

Advisers:
Eden Delight P. Miro, PhD
Ateneo de Manila University
Luis S. Silvestre Jr., PhD
Ateneo de Manila University

Panelists:
Philipp Gohlke, PhD (Critic Reader)
Lund University
Job A. Nable, PhD
Ateneo de Manila University
Timothy Robin Y. Teng, PhD
Ateneo de Manila University

In this study, we extend diffraction calculations made by Spindeler (2017) and Gohlke (2017) to a family of constant-shaped random substitutions of one and two dimensions. Specifically, we will consider a family of binary random substitutions defined by the rule
 

sures. We show that it has a mixed spectral type consisting of a pure point part and an absolutely continuous part, using theory in Gohlke (2021). Moreover, we find an explicit formula for the pure point part, which determines the set of Bragg peaks, and an explicit formula for the absolutely continuous part.

Key Words: diffraction, diffraction measure, random substitutions, symbolic dynamics