Andy Heeszel
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About Me
About Me
I am a PhD student in statistics department working with David Sivakoff. I will graduate in May 2026. My research specializes in applied probability and interacting particle systems.
Research
Research
My primary research interests are in applied probability, interacting particle systems, and Markov chain mixing times.
An interacting particle system is a probability model where nodes on a graph interact with dependencies based on their neighbors. Although there are strong dependencies in the activities between sites locally, many times we see mixing behavior and quick rates of decay in the dependencies between sites as we vary the distance or time between them. Often small perturbations to models can cause meaningful changes to these rates of decay.
I have completed projects on the boundary modified contact process, and showing cutoff in the mixing time of families of random walks on the discrete torus via their correlation structure. (See Preprints and Submitted Manuscripts).
Boundary Modified Contact Process:
In [2] I answer an open conjecture by showing a law of large numbers and functional central limit theorem for the right edge process of the boundary modified contact process. In the contact process models an outbreak on a contact network where sites jump between being susceptible and infected. Infected sites infected their neighbors at an infection rate λ, and recover at rate 1.
The outbreak on boundary modified contact process spreads across the integer lattice. The boundary between the leftmost and rightmost infected edges has a separate infection rate λe, compared to the interior infection rate λi. I studied the regime when λi = λc, the critical infection rate of the contact process, and λe > λi. This adds challenges in studying the model due to a loss of attractiveness, and since the contact process cannot sustain the infection indefinitely at criticality.
Figure 1: Trajectory of a boundary modified contact process in two dimensions where the topmost infected site on the line x = 0 has infection rate 0.75, while the infection rate of all other sites is at criticality.
Figure 2: Trajectory of the one dimensional boundary modified contact process with an exterior infection rate of 2, and interior infection rate at criticality.
Preprints and Submitted Manuscripts:
[2] Andrew Heeszel. Edge speeds and fluctuations for the one-dimensional boundary modified contact process with exterior edge boosts. In preparation, 2025.
[1] Zihao Fang and Andrew Heeszel. Cutoff for contingency table random walks. preprint on arXiv https://arxiv.org/abs/2407.16203
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