Scaling Limits of Critical Observables Through the High Dimensional Incipient Infinite Cluster

Author

• Pranav Chinmay, CUNY Graduate CenterFollow

Date of Degree

6-2026

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy

Program

Mathematics

Advisor

Jack Hanson

Committee Members

Louis-Pierre Arguin

Shirshendu Chatterjee

Elena Kosygina

Subject Categories

Probability

Keywords

Percolation, Probability Theory, Statistical Mechanics

Abstract

We give a general construction of the incipient infinite cluster in high dimensional percolation, and use it as a decoupling tool to rigorize geometric heuristics for analyzing the asymptotics of observables at criticality. Examples include demonstrating the limiting distribution of the chemical distance and full-strength asymptotics for k-point functions, which constitute foundational inputs for scaling limit results associated to critical clusters.

Recommended Citation

Chinmay, Pranav, "Scaling Limits of Critical Observables Through the High Dimensional Incipient Infinite Cluster" (2026). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/6666