Random words, Toeplitz determinants and integrable systems: II
نویسندگان
چکیده
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
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.
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 کاملToeplitz Determinants, Random Growth and Determinantal Processes
We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory. 2000 Mathematics Subject Classification: 60C05.
متن کاملPowers of large random unitary matrices and Toeplitz determinants
We study the limiting behavior of TrUk(n), where U is a n × n random unitary matrix and k(n) is natural number that may vary with n in an arbitrary way. Our analysis is based on the connection with Toeplitz determinants. The central observation of this paper is a strong Szegö limit theorem for Toeplitz determinants associated to symbols depending on n in a particular way. As a consequence to th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2001
ISSN: 0167-2789
DOI: 10.1016/s0167-2789(01)00171-3