Random Words, Toeplitz Determinants, and Integrable Systems I
نویسندگان
چکیده
It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles subject to an overall constraint that the eigenvalues lie in a hyperplane.
منابع مشابه
Random words, Toeplitz determinants and integrable systems: II
This paper connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemnn-Hilbert problem and an associated system of integrable partial differential equations. In particular, we show that the Poissonization of the distribution function of this length can be identified as the Jimbo-Miwa-Ueno tau function. © 2001 Elsevier Science B.V. A...
متن کاملRandom words, Toeplitz determinants and integrable systems. I, preprint (arXiv: math.CO/9909169
This paper, a continuation of [16], connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemann-Hilbert problem and an associated system of integrable PDEs. That such a connection exists is not so surprising given the fundamental work of Baik, Deift and Johansson [3] connecting the related problem involving random permutations to a...
متن کاملIntegrable Lattices : Random Matrices and Random Permutations ∗ Pierre
These lectures present a survey of recent developments in the area of random matrices (finite and infinite) and random permutations. These probabilistic problems suggest matrix integrals (or Fredholm determinants), which arise very naturally as integrals over the tangent space to symmetric spaces, as integrals over groups and finally as integrals over symmetric spaces. An important part of thes...
متن کاملBlock Toeplitz determinants , constrained KP and Gelfand - Dickey hierarchies
We propose a method for computing any Gelfand-Dickey τ function living in SegalWilson Grassmannian as the asymptotics of block Toeplitz determinant associated to a certain class of symbols W(t; z). Also truncated block Toeplitz determinants associated to the same symbols are shown to be τ function for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from ...
متن کاملar X iv : m at h - ph / 0 11 10 08 v 1 5 N ov 2 00 1 DISCRETE GAP PROBABILITIES AND DISCRETE PAINLEVÉ EQUATIONS
We prove that Fredholm determinants of the form det(1 − Ks), where Ks is the restriction of either the discrete Bessel kernel or the discrete 2F1 kernel to {s, s + 1, . . . }, can be expressed through solutions of discrete Painlevé II and V equations, respectively. These Fredholm determinants can also be viewed as distribution functions of the first part of the random partitions distributed acc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999