


























We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For operators on these graphs we derive a new variational formula for the spectral radius and provide new proofs of results due to Sunada and Aomoto using free probability. With the goal of extending the applicability of free probability techniques beyond universal covering trees, we introduce a new combinatorial product operation on graphs and show that, in the non-commutative probability context, it corresponds to the notion of freeness with amalgamation. We show that Cayley graphs of amalgamated free products of groups, as well as universal covering trees, can be constructed using our graph product.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。