Title:
A central limit type conjecture for the nodal statistics of quantum graphs
Abstract:
The nodal distribution of a given standard quantum graph have been shown to hold information about the topology of the graph, and it was explicitly calculated for specific families of graphs. In all of those cases, and in any numerical simulation, the nodal statistics appears to obey a central limit type convergence to a normal distribution as the number of edges (more specifically, the first Betti number) goes to infinity. We conjecture that this central limit type convergence of the nodal statistics is a universal property of quantum graphs. In the talk I will define the nodal statistics, state the conjecture and describe the proof of convergence for specific families of graphs. This talk is based on Joint work with Ram Band and Gregory Berkolaiko.