Adithya P. 2026 | BASIS Independent McLean
- Project Title: A Standard Schelling Model
- BASIS Independent Advisor: Aaron Glanzer
- Internship Location: Mason Experimental Geometry Lab
- Onsite Mentor: Professor Michael Jarret
In this project, we introduce a unifying framework for Schelling-type segregation models. They are defined as parametrized probility distributions on a graph using the Metropolis-Hastings distribution with specificed proposal and acceptance distributions. The framework extends to multiple demographies and vacancy types. We further provide a "practitioner's cookbook" that reframes examples like Schelling 1971 and Ising’s Model as different proposal-accept distributions. The cookbook is such that changing the ingredients creates a better recipe (a type of model).
My Posts
Week 8: Non-Schelling Models
May 5, 2026
It turns out that one of the reasons why developing precise mathematics for these models was crucial is that many of the models resembling Schelling’s do not hold up under closer examination. First, there is the issue of “reducibility,” meaning that the simulation gets “stuck.” Classical Schelling models iterate over each agent until all are […]
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Week 7: Full Simulation in Code!
April 29, 2026
This week marked the first time that I truly experienced the full capabilities of our code! I created a Metropolis-Hastings algorithm on a lattice structure and let it iterate until the next iteration wouldn’t provide a better energy state. In the random case I chose that meant 10,000 times. As expected, the result proved accurate […]
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Week 6: Implications and Process
April 23, 2026
This week, I’m going to step back and explain a bit more about what a Schelling Model is and why it matters. What does a Schelling Model entail? In our new framework, “Schelling models” will mean Metropolis-Hastings Markov chains. Here is how you might conceptualize it: instead of cumbersome agent-based simulations with absorbing states, everything […]
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Week 5: Simulation and Explanation
April 15, 2026
With a simulation created, now would be the ideal time to take a step back and delve into exactly what is going on, especially since a term like “Metropolis-Hastings Schelling simulation” sounds complicated when really, it’s a pretty simple concept. Consider a grid where people are either red or blue and have only one preference […]
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