Singularity of Some Random Continued Fractions
Russell Lyons
TL;DR
This paper proves the singularity of certain distributions of random continued fractions linked to iterated function systems with overlap and a parabolic point, arising from the study of Galton-Watson tree conductance.
Contribution
It establishes the singularity of specific random continued fraction distributions associated with complex iterated function systems.
Findings
Proves singularity of distributions in complex systems with overlaps.
Connects continued fractions to conductance in Galton-Watson trees.
Provides new insights into the behavior of random continued fractions.
Abstract
We prove singularity of some distributions of random continued fractions that correspond to iterated function systems with overlap and a parabolic point. These arose while studying the conductance of Galton-Watson trees.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Theoretical and Computational Physics