Mondays at 2pm
Frank Adams 1, Alan Turing Building
Contacts Donald Robertson Yotam Smilansky
The independence polynomial for recursive graph sequences: the dynamical perspective
Misha Hlushchanka
University of Amsterdam
The distribution of zeros of partition functions on graphs is intimately related to the analyticity of physical quantities and their phase transitions. The independence polynomial of a finite graph is the generating function for the numbers of independent sets (i.e., subsets of pairwise non-adjacent vertices) of each size. It naturally originates in statistical physics as the partition function of the hard-core model for gases, where each particle occupies an exclusive region of space. It is known that the roots of the independence polynomial are dense outside a neighborhood of the origin for the family of bounded-degree graphs. However, the overall structure of this zero locus, as well as the corresponding zero locus for concrete sequences of graphs, may be quite intricate. Jointly with Han Peters (University of Amsterdam), we develop a unified dynamical framework for the analysis of these zero sets for recursive graph sequences. In the talk, I will report on our results concerning their structure, with particular emphasis on (the absence of) phase transitions.