6,404 research outputs found
Longest increasing subsequences of random colored permutations
We compute the limit distribution for (centered and scaled) length of the
longest increasing subsequence of random colored permutations. The limit
distribution function is a power of that for usual random permutations computed
recently by Baik, Deift, and Johansson (math.CO/9810105). In two--colored case
our method provides a different proof of a similar result by Tracy and Widom
about longest increasing subsequences of signed permutations (math.CO/9811154).
Our main idea is to reduce the `colored' problem to the case of usual random
permutations using certain combinatorial results and elementary probabilistic
arguments.Comment: AMSTeX, 11 page
Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
We consider the totally asymmetric simple exclusion process, a model in the
KPZ universality class. We focus on the fluctuations of particle positions
starting with certain deterministic initial conditions. For large time t, one
has regions with constant and linearly decreasing density. The fluctuations on
these two regions are given by the Airy_1 and Airy_2 processes, whose one-point
distributions are the GOE and GUE Tracy-Widom distributions of random matrix
theory. In this paper we analyze the transition region between these two
regimes and obtain the transition process. Its one-point distribution is a new
interpolation between GOE and GUE edge distributions.Comment: 28 pages, 5 figures, LaTe
Schur dynamics of the Schur processes
We construct discrete time Markov chains that preserve the class of Schur
processes on partitions and signatures.
One application is a simple exact sampling algorithm for
q^{volume}-distributed skew plane partitions with an arbitrary back wall.
Another application is a construction of Markov chains on infinite
Gelfand-Tsetlin schemes that represent deterministic flows on the space of
extreme characters of the infinite-dimensional unitary group.Comment: 22 page
Loop-free Markov chains as determinantal point processes
We show that any loop-free Markov chain on a discrete space can be viewed as
a determinantal point process. As an application, we prove central limit
theorems for the number of particles in a window for renewal processes and
Markov renewal processes with Bernoulli noise.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP115 the Annales de
l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques
(http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics
(http://www.imstat.org
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