Myopic non-intersecting Brownian motions in a periodic potential converge, as the potential and foresight grow together, to myopic non-intersecting random walks that interpolate between TASEP and non-colliding Poisson walks.
Why random matrices share universal processes with interacting particle systems?
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abstract
In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy_2 process, arise both in random matrices and interacting particle systems. The link is through a common mathematical structure on an interlacing structure, also known as Gelfand-Tsetlin pattern, that appears for specific models in both fields.
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Myopic non-intersection in a periodic potential
Myopic non-intersecting Brownian motions in a periodic potential converge, as the potential and foresight grow together, to myopic non-intersecting random walks that interpolate between TASEP and non-colliding Poisson walks.