3 papers
math.LO2026
Spectral Theory for Borel PMP Graphs
Cecelia Higgins, Pieter Spaas, Alexander Tenenbaum
We initiate a systematic study of spectral theory for bounded-degree Borel pmp graphs. Specifically, we study spectral properties of the associated adjacency and Laplacian operator…
math.LO2026
Measurable Brooks's Theorem for Directed Graphs
Cecelia Higgins
We prove a descriptive version of Brooks's theorem for directed graphs. In particular, we show that, if is a Borel directed graph on a standard Borel space such that the ma…
math.LO2026
Complexity of Finite Borel Asymptotic Dimension
Jan GrebÃk, Cecelia Higgins
We show that the set of locally finite Borel graphs with finite Borel asymptotic dimension is -complete. The result is based on a combinatorial characterization of f…