1,524 research outputs found
Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
In [arXiv:0804.3035] we studied an interacting particle system which can be
also interpreted as a stochastic growth model. This model belongs to the
anisotropic KPZ class in 2+1 dimensions. In this paper we present the results
that are relevant from the perspective of stochastic growth models, in
particular: (a) the surface fluctuations are asymptotically Gaussian on a
sqrt(ln(t)) scale and (b) the correlation structure of the surface is
asymptotically given by the massless field.Comment: 13 pages, 4 figure
Infinite-dimensional diffusions as limits of random walks on partitions
The present paper originated from our previous study of the problem of
harmonic analysis on the infinite symmetric group. This problem leads to a
family {P_z} of probability measures, the z-measures, which depend on the
complex parameter z. The z-measures live on the Thoma simplex, an
infinite-dimensional compact space which is a kind of dual object to the
infinite symmetric group. The aim of the paper is to introduce stochastic
dynamics related to the z-measures. Namely, we construct a family of diffusion
processes in the Toma simplex indexed by the same parameter z. Our diffusions
are obtained from certain Markov chains on partitions of natural numbers n in a
scaling limit as n goes to infinity. These Markov chains arise in a natural
way, due to the approximation of the infinite symmetric group by the increasing
chain of the finite symmetric groups. Each z-measure P_z serves as a unique
invariant distribution for the corresponding diffusion process, and the process
is ergodic with respect to P_z. Moreover, P_z is a symmetrizing measure, so
that the process is reversible. We describe the spectrum of its generator and
compute the associated (pre)Dirichlet form.Comment: AMSTex, 33 pages. Version 2: minor changes, typos corrected, to
appear in Prob. Theor. Rel. Field
Statistics of layered zigzags: a two-dimensional generalization of TASEP
A novel discrete growth model in 2+1 dimensions is presented in three
equivalent formulations: i) directed motion of zigzags on a cylinder, ii)
interacting interlaced TASEP layers, and iii) growing heap over 2D substrate
with a restricted minimal local height gradient. We demonstrate that the
coarse-grained behavior of this model is described by the two-dimensional
Kardar-Parisi-Zhang equation. The coefficients of different terms in this
hydrodynamic equation can be derived from the steady state flow-density curve,
the so called `fundamental' diagram. A conjecture concerning the analytical
form of this flow-density curve is presented and is verified numerically.Comment: 5 pages, 4 figure
Universal exit probabilities in the TASEP
We study the joint exit probabilities of particles in the totally asymmetric
simple exclusion process (TASEP) from space-time sets of given form. We extend
previous results on the space-time correlation functions of the TASEP, which
correspond to exits from the sets bounded by straight vertical or horizontal
lines. In particular, our approach allows us to remove ordering of time moments
used in previous studies so that only a natural space-like ordering of particle
coordinates remains. We consider sequences of general staircase-like boundaries
going from the northeast to southwest in the space-time plane. The exit
probabilities from the given sets are derived in the form of Fredholm
determinant defined on the boundaries of the sets. In the scaling limit, the
staircase-like boundaries are treated as approximations of continuous
differentiable curves. The exit probabilities with respect to points of these
curves belonging to arbitrary space-like path are shown to converge to the
universal Airy process.Comment: 46 pages, 7 figure
From interacting particle systems to random matrices
In this contribution we consider stochastic growth models in the
Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large
time distribution and processes and their dependence on the class on initial
condition. This means that the scaling exponents do not uniquely determine the
large time surface statistics, but one has to further divide into subclasses.
Some of the fluctuation laws were first discovered in random matrix models.
Moreover, the limit process for curved limit shape turned out to show up in a
dynamical version of hermitian random matrices, but this analogy does not
extend to the case of symmetric matrices. Therefore the connections between
growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor
corrections in scaling of section 2.
Convective Term and Transversely Driven Charge-Density Waves
We derive the convective terms in the damping which determine the structure
of the moving charge-density wave (CDW), and study the effect of a current
flowing transverse to conducting chains on the CDW dynamics along the chains.
In contrast to a recent prediction we find that the effect is orders of
magnitude smaller, and that contributions from transverse currents of electron-
and hole-like quasiparticles to the force exerted on the CDW along the chains
act in the opposite directions. We discuss recent experimental verification of
the effect and demonstrate experimentally that geometry effects might mimic the
transverse current effect.Comment: RevTeX, 9 pages, 1 figure, accepted for publications in PR
Airy processes and variational problems
We review the Airy processes; their formulation and how they are conjectured
to govern the large time, large distance spatial fluctuations of one
dimensional random growth models. We also describe formulas which express the
probabilities that they lie below a given curve as Fredholm determinants of
certain boundary value operators, and the several applications of these
formulas to variational problems involving Airy processes that arise in
physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI
Proceedings: Topics in percolative and disordered systems
The research of functioning of the human cardiovascular system within the zones of active geological faults of the city of Gorno-Altaisk
A Time-Space Tradeoff for Triangulations of Points in the Plane
In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm
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