Speaker: Lacie Lynch (UCF, Mathematics Department)
Title: Diffusion in systems of colliding particles
Abstract: When modeling diffusion, we often think of an idealized process where particles move freely, spreading out in a way that can be described by a partial differential equation. This behavior can also be understood probabilistically in terms of Brownian motion, where each particle follows an independent random trajectory. However, in many physical systems, particles are not entirely unimpeded as they disperse. Instead, they interact through collisions, requiring some sort of prescribed rule to govern their behavior upon meeting.
In 1965, Harris introduced a colliding particle model in which Brownian particles are prohibited from passing one another during interactions. The effect of constraining their interactions in this way leads to subdiffusive behavior, where the spreading of a tagged particle—a particle that is identified and tracked over time-scales more slowly than that of unconstrained Brownian motion. In 2007, Swanson observed the same type of scaling under a different model, where themedian of a collection of independent Brownian motions behaves like a tagged particle. The median process naturally enforces an ordering constraint, restricting motion in a way reminiscent of Harris’s model.
This talk will focus on the setup of Harris’s model and the analogous aspects of Swanson’s model, time permitting.
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