| 概要 | In this talk, I will discuss joint work with Ben Hambly (Oxford)
regarding the high frequency asymptotics of the eigenvalue counting
function
associated with the natural Dirichlet form on alpha-stable trees,
which lead in turn to short-time heat kernel asymptotics for these random
structures. In particular, I will explain how our results are proved using
self-similar fractal arguments that involve decomposing the relevant tree
into three pieces in the alpha=2 case and a countable number of pieces
otherwise. The talk will also include a brief discussion of how these ideas
can be adapted to the scaling limit of the critical random graph. |