Computing inverses of Stieltjes transforms of probability measures
File(s)
Accepted version
Author(s)
Chen, James
Olver, Sheehan
Type
Journal Article
Abstract
The Stieltjes (or sometimes called the Cauchy) transform is a fundamental object associated with probability measures, corresponding to the generating function of the moments. In certain applications such as free probability it is essential to compute the inverses of the Stieltjes transform, which might be multivalued. This paper establishes conditions bounding the number of inverses based on properties of the measure which can be combined with contour integral-based root finding algorithms to rigorously compute all inverses.
Date Issued
2026-01-14
Date Acceptance
2025-08-26
Citation
Mathematics of Computation, 2026
ISSN
0025-5718
Publisher
American Mathematical Society
Journal / Book Title
Mathematics of Computation
Copyright Statement
©2026 American Mathematical Society. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published online
Date Publish Online
2026-01-14