5 papers
The Random-Cluster Model on Wired Trees: Uniqueness and Negative Dependence
Heehyun Park
The random-cluster model with cluster weight is expected to exhibit negative dependence, but without FKG even pairwise negative correlation remains open on general graphs.…
Uniqueness and Mixing in the Low-Temperature Random-Cluster Model on Trees and Random Graphs
Antonio Blanca, Reza Gheissari, Heehyun Park +1
We study the random-cluster model on trees and treelike graphs at low temperatures. This is a model of dependent percolation parametrized by an edge probability and a…
Bridging the Know-Act Gap via Task-Level Autoregressive Reasoning
Jihyun Janice Ahn, Ryo Kamoi, Berk Atil +34
LLMs often generate seemingly valid answers to flawed or ill-posed inputs. This is not due to missing knowledge: under discriminative prompting, the same models can mostly identify…
Stable Vectorization of Persistent Laplacians via Spectral Descriptors
Inkee Jung, Wonwoo Kang, Heehyun Park
Persistence images vectorize persistence diagrams into stable, finite-dimensional features. Inspired by this idea, we developed a vectorization framework for the spectral informati…
Accelerated Evaluation of Ollivier-Ricci Curvature Lower Bounds: Bridging Theory and Computation
Wonwoo Kang, Heehyun Park
Curvature serves as a potent and descriptive invariant, with its efficacy validated both theoretically and practically within graph theory. We employ a definition of generalized Ri…