367 research outputs found
Shape Fluctuations and Random Matrices
We study a certain random groeth model in two dimensions closely related to
the one-dimensional totally asymmetric exclusion process. The results show that
the shape fluctuations, appropriately scaled, converges in distribution to the
Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.Comment: Revised version. 51 page
Non-intersecting, simple, symmetric random walks and the extended Hahn kernel
Consider particles performing simple, symmetric, non-intersecting random
walks, starting at points , at time 0 and ending at
at time . This can also be interpreted as a random rhombus
tiling of an -hexagon, or as a random boxed planar partition confined to a
rectangular box with side lengths , and . The positions of the
particles at all times gives a determinantal point process with a correlation
kernel given in terms of the associated Hahn polynomials. In a suitable scaling
limit we obtain non-intersecting Brownian motions which can be related to
Dysons's Hermitian Brownian motion via a suitable transformation.Comment: 13 page
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