Limit theorems for height fluctuations in
a class of discrete space and time growth models I & II.
Craig Tracy and Harold Widom
Abstract:
We introduce three classes of discrete space
and discrete time growth models that are described by
a certain random height function. We formulate an equivalent
space-time path description and show for a subset of
these models that the Robinson-Schensted-Knuth bijection
provides an equivalent formulation in terms of Young tableaux.
This formulation in turn then leads to a Fredholm determinant
representation of the distribution function of the height
function. By use of rigorous saddle point methods we then
derive various limit theorems for an appropriately centered
and normalized height function. We conclude with a discussion
of the universality of these limit theorems.