1,707 research outputs found
Generalized Green Functions and current correlations in the TASEP
We study correlation functions of the totally asymmetric simple exclusion
process (TASEP) in discrete time with backward sequential update. We prove a
determinantal formula for the generalized Green function which describes
transitions between positions of particles at different individual time
moments. In particular, the generalized Green function defines a probability
measure at staircase lines on the space-time plane. The marginals of this
measure are the TASEP correlation functions in the space-time region not
covered by the standard Green function approach. As an example, we calculate
the current correlation function that is the joint probability distribution of
times taken by selected particles to travel given distance. An asymptotic
analysis shows that current fluctuations converge to the process.Comment: 46 pages, 3 figure
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
Changing Bases: Multistage Optimization for Matroids and Matchings
This paper is motivated by the fact that many systems need to be maintained
continually while the underlying costs change over time. The challenge is to
continually maintain near-optimal solutions to the underlying optimization
problems, without creating too much churn in the solution itself. We model this
as a multistage combinatorial optimization problem where the input is a
sequence of cost functions (one for each time step); while we can change the
solution from step to step, we incur an additional cost for every such change.
We study the multistage matroid maintenance problem, where we need to maintain
a base of a matroid in each time step under the changing cost functions and
acquisition costs for adding new elements. The online version of this problem
generalizes online paging. E.g., given a graph, we need to maintain a spanning
tree at each step: we pay for the cost of the tree at time
, and also for the number of edges changed at
this step. Our main result is an -approximation, where is
the number of elements/edges and is the rank of the matroid. We also give
an approximation for the offline version of the problem. These
bounds hold when the acquisition costs are non-uniform, in which caseboth these
results are the best possible unless P=NP.
We also study the perfect matching version of the problem, where we must
maintain a perfect matching at each step under changing cost functions and
costs for adding new elements. Surprisingly, the hardness drastically
increases: for any constant , there is no
-approximation to the multistage matching maintenance
problem, even in the offline case
Finding the Median (Obliviously) with Bounded Space
We prove that any oblivious algorithm using space to find the median of a
list of integers from requires time . This bound also applies to the problem of determining whether the median
is odd or even. It is nearly optimal since Chan, following Munro and Raman, has
shown that there is a (randomized) selection algorithm using only
registers, each of which can store an input value or -bit counter,
that makes only passes over the input. The bound also implies
a size lower bound for read-once branching programs computing the low order bit
of the median and implies the analog of for length oblivious branching programs
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
On the Inelastic Collapse of a Ball Bouncing on a Randomly Vibrating Platform
We study analytically the dynamics of a ball bouncing inelastically on a
randomly vibrating platform, as a simple toy model of inelastic collapse. Of
principal interest are the distributions of the number of flights n_f till the
collapse and the total time \tau_c elapsed before the collapse. In the strictly
elastic case, both distributions have power law tails characterised by
exponents which are universal, i.e., independent of the details of the platform
noise distribution. In the inelastic case, both distributions have exponential
tails: P(n_f) ~ exp[-\theta_1 n_f] and P(\tau_c) ~ exp[-\theta_2 \tau_c]. The
decay exponents \theta_1 and \theta_2 depend continuously on the coefficient of
restitution and are nonuniversal; however as one approches the elastic limit,
they vanish in a universal manner that we compute exactly. An explicit
expression for \theta_1 is provided for a particular case of the platform noise
distribution.Comment: 32 page
The impact of the publication of non-financial statements on the financial performance of companies with the identification of interpectoral features
The purpose of this article is to study the impact of the publication of non-financial statements on the financial performance of Russian companies with the identification of intersectoral feature
How long does it take to pull an ideal polymer into a small hole?
We present scaling estimates for characteristic times and
of pulling ideal linear and randomly branched polymers of
monomers into a small hole by a force . We show that the absorbtion process
develops as sequential straightening of folds of the initial polymer
configuration. By estimating the typical size of the fold involved into the
motion, we arrive at the following predictions: and , and we also confirm them by
the molecular dynamics experiment.Comment: 4 pages, 3 figure
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