Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity

We report some new observation concerning the statistics of Longest Increasing Subsequences (LIS). We show that the expectation of LIS, its variance, and apparently the full distribution function appears in statistical analysis of some simple nonlinear stochastic partial differential equation (SPDE) in the limit of very low noise intensity.Comment: 6 pages, 4 figures, reference adde

Solution of the infinite range t-J model

The t-J model with constant t and J between any pair of sites is studied by exploiting the symmetry of the Hamiltonian with respect to site permutations. For a given number of electrons and a given total spin the exchange term simply yields an additive constant. Therefore the real problem is to diagonalize the "t- model", or equivalently the infinite U Hubbard Hamiltonian. Using extensively the properties of the permutation group, we are able to find explicitly both the energy eigenvalues and eigenstates, labeled according to spin quantum numbers and Young diagrams. As a corollary we also obtain the degenerate ground states of the finite $U$ Hubbard model with infinite range hopping -t>0.Comment: 15 pages, 2 figure

The Algebra of Binary Search Trees

We introduce a monoid structure on the set of binary search trees, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion. This leads to a new construction of the algebra of Planar Binary Trees of Loday-Ronco, defining it in the same way as Non-Commutative Symmetric Functions and Free Symmetric Functions. We briefly explain how the main known properties of the Loday-Ronco algebra can be described and proved with this combinatorial point of view, and then discuss it from a representation theoretical point of view, which in turns leads to new combinatorial properties of binary trees.Comment: 49 page

Expected length of the longest common subsequence for large alphabets

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe

KPZ equation in one dimension and line ensembles

For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through which such results are obtained, namely the method of line ensembles with purely entropic repulsion.Comment: Proceedings STATPHYS22, Bangalore, 200

Intermediate coupling fixed point study in the overscreened regime of generalized multichannel SU(N) Kondo models

We study a generalized multichannel single-impurity Kondo model, in which the impurity spin is described by a representation of the SU(N) group which combines bosonic and fermionic degrees of freedom. The impurity spin states are described by Abrikosov pseudofermions, and we make use of a method initiated by Popov and Fedotov which allows a proper handling of the fermionic constraint. The partition function is derived within a path integral approach. We use renormalization group techniques to calculate the $\beta$ scaling function perturbatively in powers of the Kondo coupling constant, which is justified in the weak coupling limit. The truncated expansion is valid in the overscreened (Nozieres-Blandin) regime, for an arbitrary SU(N) group and any value of the parameters characterizing the impurity spin representation. The intermediate coupling fixed point is identified. We derive the temperature dependence of various physical quantities at low T, controlled by a unique critical exponent, and show that the physics of the system in the overscreened regime governed by the intermediate coupling fixed point is characterized by a non-Fermi liquid behavior. Our results are in accordance with those obtained by other methods, as Bethe ansatz and boundary conformal field theory, in the case of various impurity spin symmetries. We establish in a unified way that the Kondo models in which the impurity spin is described successively by a fundamental, symmetric, antisymmetric and mixed symmetry representation yield all the same low-energy physics in the overscreened regime. Possible generalizations of the analysis we present to the case of arbitrary impurity spin representations of SU(N) are also discussed.Comment: 21 pages, 7 figures, REVTeX; final version accepted for publicatio

Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization

Coherence in an open quantum system is degraded through its interaction with a bath. This decoherence can be avoided by restricting the dynamics of the system to special decoherence-free subspaces. These subspaces are usually constructed under the assumption of spatially symmetric system-bath coupling. Here we show that decoherence-free subspaces may appear without spatial symmetry. Instead, we consider a model of system-bath interactions in which to first order only multiple-qubit coupling to the bath is present, with single-qubit system-bath coupling absent. We derive necessary and sufficient conditions for the appearance of decoherence-free states in this model, and give a number of examples. In a sequel paper we show how to perform universal and fault tolerant quantum computation on the decoherence-free subspaces considered in this paper.Comment: 18 pages, no figures. Major changes. Section on universal fault tolerant computation removed. This section contained a crucial error. A new paper [quant-ph/0007013] presents the correct analysi

A Matrix model for plane partitions

We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP-like process with arbitrary boundary conditions. Using the known solution of matrix models, this method allows to find the large size asymptotic expansion of plane partitions, to ALL orders. It also allows to describe several universal regimes.Comment: Latex, 41 figures. Misprints and corrections. Changing the term TASEP to self avoiding particle porces

Genome amplification and gene expression in the ciliate macronucleus

The focus of this review is on the micronucleus and macronucleus in the ciliated protozoa and the organization and function of the DNA molecules within them. We present (1) some of the structural and functional differences which are known, (2) the genetic evidence for macronuclear units, (3) two hypotheses for the organization of the DNA molecules in the macronucleus to explain these units, and (4) experiments designed to discriminate between these hypotheses. We conclude that the size of the genome is not reduced in the macronucleus and that there are 45 copies of the haploid genome present in the macronucleus of normal strains of Tetrahymena pyriformis and 800 copies in the macronucleus of Paramecium aurelia . The ciliate genome is relatively simple in terms of repeated sequences. However, not all copies of the genes present in the macronucleus may be identical since fractions of differing thermal stability appear after renaturation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44178/1/10528_2004_Article_BF00486122.pd

Electromagnetic and Acoustic Scattering by a Semi‐Infinite Body of Revolution

The first two terms of Kline's asymptotic expansion are obtained for the scattering of a plane wave incident along the axis of a perfectly reflecting semi‐infinite body of revolution. When this method is applied to the paraboloid the exact electromagnetic solution is obtained in closed form. The accuracy of the method of physical optics is studied by using the asymptotic expansion.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69381/2/JAPIAU-26-3-306-1.pd