Bachelor's Thesis: Mixing under Monotone Censoring

A literature and simulation study of lazy random walks on large monotone subsets of the hypercube, working from the prior O(n³) mixing-time bound.

The question

With Pratham Pekamwar and under Dr. Benny George K’s supervision at IIT Guwahati, I studied lazy simple random walks on monotone subsets (V \subseteq {0,1}^n) containing at least half of the hypercube.

The project examined the earlier (O(n^3)) upper bound and the path toward the conjectured (O(n \log n)) behaviour. It did not claim a new proof. We surveyed coupling, censoring, and strong-stationary-time techniques and built a Python simulation framework over explicit transition matrices to understand where the structure of the subset makes a tighter analysis difficult.