190 citations · 1.9k across the 70 of their papers we have counts for
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A growth model in a random environment
Janko Gravner, Craig A. Tracy, Harold Widom
We consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update ru…
A Distribution Function Arising in Computational Biology
Craig A. Tracy, Harold Widom
Karlin and Altschul in their statistical analysis for multiple high-scoring segments in molecular sequences introduced a distribution function which gives the probability there are…
Determinants of Hankel Matrices
Estelle L. Basor, Yang Chen, Harold Widom
The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval.The main idea is to reduce the problem to dete…
Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models
Janko Gravner, Craig A. Tracy, Harold Widom
We introduce a class of one-dimensional discrete space-discrete time stochastic growth models described by a height function with corner initialization. We prove, with one…
Random Words, Toeplitz Determinants and Integrable Systems. II
Alexander R. Its, Craig A. Tracy, Harold Widom
This paper, a continuation of math.CO/9909169, connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemann-Hilbert p…