Brownian Motion Applied to Human Intersections
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In this paper, we will adapt Einstein's work on Brownian Motion to pedestrian movement and then use that information to prove three hypotheses: 1) In general, pedestrian movement at an intersection is not a Brownian Motion. 2) Pedestrian movement at intersections in high density cities is a Brownian Motion. 3) Pedestrian movement at intersections on a university campus during normal business hours on normal business days is a Brownian Motion. We will attempt this by examining the concept of Brownian Motion as presented by three of its main founders, Brown, Weiner, and Einstein, as well as many applications, and then summarizing Einstein's work on developing a diffusivity coefficient. We will then adapt Einstein's Brownian Coefficient of Diffusivity from the molecular case to pedestrian movement. It is during this process that we will prove or disprove our three hypotheses. Finally, we will analyze video logs to determine if the theory holds, and if not, then why it failed.