Title

Counting and Partition Function Asymptotics for Subordinate Killed Brownian Motion

Document Type

Book Chapter

Publication Date

2016

Department

Mathematics

Language

English

Publication Title

Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium

Abstract

We consider the subordinate killed Brownian motion process generated by first killing Brownian motion at some boundary point on a smooth bounded domain then subordinating by a Lévy time-clock. For classes of subordinators satisfying some growth requirements, we establish asymptotic growth for the eigenvalues associated to these processes. Using an abelian argument we are then able to prove first-term asymptotics for the trace of the heat semigroup, or partition function. For α/2-stable subordinators we prove second-order term asymptotics of the partition function with constants dependent on volume and surface area of the boundary.

Comments

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