Research
My research studies rare events in random discrete structures, with a particular focus on subgraph counts, conditioned structure, and sampling in sparse random graphs.
Research Output
Preprint | September 2026
Jade Lintott, Will Perkins, and Corrine Yap
We give first-order asymptotics for local lower-tail probabilities of triangle counts in sparse random graphs, characterize the conditional distribution of the triangle set, and give an efficient algorithm to approximately sample from the conditional graph distribution.
Invited talks
Dissertation Research
Imagine a network in which each pair of vertices is connected at random. A triangle appears when three vertices are all connected to one another. My dissertation studies sparse networks with unusually few of these small patterns: how likely they are, what their triangles look like, and how to generate examples efficiently.
The word local refers to asking for an exact count, rather than a range of counts. My work connects precise probability estimates with descriptions of how triangles overlap, using that understanding to develop approximate sampling algorithms. More broadly, I am interested in how rare events shape random combinatorial structures.
Advisor: Will Perkins · PhD expected May 2027
Projects
Note on ongoing work. This page omits collaborations in progress because of concerns about preliminary results being scooped using large language models (LLMs).
Current preprint
My work with Will Perkins and Corrine Yap studies local lower-tail asymptotics for triangle counts and a transition in the conditioned distribution of triangles in sparse random graphs.
Broader program
A central goal of my work is to describe the structures that realize rare events and use those descriptions to design efficient approximate sampling methods.
Next directions
I am interested in extending these ideas to more general subgraphs and to wider families of sparse random structures.
Research Profile