David Clancy, Jr.

About Me

I'm David Clancy, Jr. I'm currently a Van Vleck postdoc in the Department of Mathematics at the University of Wisconsin at Madison and a Research Assistant at the Institute for Foundations of Data Science. I am working with Hanbaek Lyu and Sebastien Roch.

I completed my Ph.D. at the University of Washington under the supervision of Soumik Pal. I did my undergrad at the University of North Carolina at Chapel Hill.

Email: djclancyjr [at] gmail [dot] com

Research Interests

My research interests lie in probability theory. More specifically, I'm interested in the large scale behavior of random graphs and random trees and interplay between continuum objects and their discrete descriptions. Recently, I have been interested in understanding the component structure of the degree corrected stochastic block model at some notion of criticality as the number of vertices in each block grows large simultaneously.

A broad thread running through my work is the interplay between depth-first descriptions and breadth-first descriptions of these discrete trees and graphs. Very often there is a way to encode information about the graph by a process (think Dyck paths) in either a depth-first or bread-first manner. Often these encodings are in some sense equal in distribution. From here, some mass structure can be obtained by random time-changes and limit theorems. This works quite well in the discrete, but it can even be done in the continuum!

Publications and Preprints

Preprints

with O. Angtuncio Hernández: Multitype Lévy trees as scaling limits of multitype Bienaymé-Galton-Watson trees. February 2025.
with H. Lyu, S. Roch: Likelihood landscape of binary latent model on a tree. January 2025.
with H. Lyu, S. Roch and A. Sly: Likelihood-Based Root State Reconstruction on a Tree: Sensitivity to Parameters and Applications. January 2025.
Fluctuations of the giant of Poisson random graphs. January 2025.
A central limit theorem for the giant in a stochastic block model. January 2025.
Asymptotics for the number of bipartite graphs with fixed surplus. November 2024.
Near-critical bipartite configuration models and their associated intersection graphs. October 2024.
Component sizes of rank-2 multiplicative random graphs. October 2024.
with V. Konarovskyi and V. Limic: Degree corrected stochastic block model: excursion representation. October 2024.
Inhomogeneous percolation on the hierarchical configuration model with a heavy-tailed degree distribution. January 2024.

with J. Choi: Occupation Times for Time-changed Processes with Applications to Parisian Options. October 2021.
Encoding multitype Galton-Watson forests and a multitype Ray-Knight theorem. Submitted. May 2021.
A new relationship between Erdős-Rényi graphs, epidemic models and Brownian motion with parabolic drift. July 2020.

Publications

with H. Lyu and S. Roch: Sample complexity of branch-length estimation by maximum likelihood. Accepted (poster) at ICML 2025. Link to camera-ready version.
Epidemics on critical random graphs with heavy-tailed degree distribution. Accepted Stochastic Processes and Applications. January 2025. arXiv version.
The Gorin-Shkolnikov identity and its random tree generalization. Accepted Journal of Theoretical Probability. August 2021. arXiv version.

Presentations and Talks

ICIAM 2023 Tokyo. Mini-symposium on "Scaling limits of interacting particle systems."
2023 IFDS annual meeting. August 2, 2023. "Reconstructing mutation rates on Binary trees."
Poster presented at 2023 Seminar in Stochastic Processes.
Probability Seminar at the University of Illinois Urbana-Champaign. December 6, 2022. "Component Sizes of degree-corrected stochastic blockmodel."
Probability Seminar at the University of Wisconsin Madison. November 10, 2022. "Component Sizes of degree-corrected stochastic blockmodel."
Probability Seminar at the University of Washington. April 26, 2021. "Epidemics on critical graphs with heavy-tailed degree distribution."
Probability Seminar at the University of Washington. October 5, 2020. “Aldous’s Brownian excursions, critical random graphs and the multiplicative coalescent."
The above talk was part of the Hidden Gems part of the Probability Seminar, where graduate students presented a groundbreaking paper in an area related to their research. My slides can be found here.
Probability Seminar at the University of Washington. October 28, 2019. “The Gorin-Shkolnikov identity and its random tree generalization.”
Data driven Problems in Mathematical Finance Session at INFORMS 2019 Annual Meeting. October 22, 2019. “The Gorin-Shkolnikov identity and its random tree generalization.”

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