3,213 research outputs found
Quantitative estimates of discrete harmonic measures
A theorem of Bourgain states that the harmonic measure for a domain in
is supported on a set of Hausdorff dimension strictly less than
\cite{Bourgain}. We apply Bourgain's method to the discrete case, i.e., to the
distribution of the first entrance point of a random walk into a subset of , . By refining the argument, we prove that for all \b>0 there
exists \rho (d,\b)N(d,\b), any , and any | \{y\in\Z^d\colon \nu_{A,x}(y)
\geq n^{-\b} \}| \leq n^{\rho(d,\b)}, where denotes the
probability that is the first entrance point of the simple random walk
starting at into . Furthermore, must converge to as \b \to
\infty.Comment: 16 pages, 2 figures. Part (B) of the theorem is ne
Conformal invariance in two-dimensional turbulence
Simplicity of fundamental physical laws manifests itself in fundamental
symmetries. While systems with an infinity of strongly interacting degrees of
freedom (in particle physics and critical phenomena) are hard to describe, they
often demonstrate symmetries, in particular scale invariance. In two dimensions
(2d) locality often promotes scale invariance to a wider class of conformal
transformations which allow for nonuniform re-scaling. Conformal invariance
allows a thorough classification of universality classes of critical phenomena
in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example
of strongly-interacting non-equilibrium system? Here, using numerical
experiment, we show that some features of 2d inverse turbulent cascade display
conformal invariance. We observe that the statistics of vorticity clusters is
remarkably close to that of critical percolation, one of the simplest
universality classes of critical phenomena. These results represent a new step
in the unification of 2d physics within the framework of conformal symmetry.Comment: 10 pages, 5 figures, 1 tabl
Random walk on the range of random walk
We study the random walk X on the range of a simple random walk on ℤ d in dimensions d≥4. When d≥5 we establish quenched and annealed scaling limits for the process X, which show that the intersections of the original simple random walk path are essentially unimportant. For d=4 our results are less precise, but we are able to show that any scaling limit for X will require logarithmic corrections to the polynomial scaling factors seen in higher dimensions. Furthermore, we demonstrate that when d=4 similar logarithmic corrections are necessary in describing the asymptotic behavior of the return probability of X to the origin
Fe I Oscillator Strengths for the Gaia-ESO Survey
The Gaia-ESO Public Spectroscopic Survey (GES) is conducting a large-scale
study of multi-element chemical abundances of some 100 000 stars in the Milky
Way with the ultimate aim of quantifying the formation history and evolution of
young, mature and ancient Galactic populations. However, in preparing for the
analysis of GES spectra, it has been noted that atomic oscillator strengths of
important Fe I lines required to correctly model stellar line intensities are
missing from the atomic database. Here, we present new experimental oscillator
strengths derived from branching fractions and level lifetimes, for 142
transitions of Fe I between 3526 {\AA} and 10864 {\AA}, of which at least 38
are urgently needed by GES. We also assess the impact of these new data on
solar spectral synthesis and demonstrate that for 36 lines that appear
unblended in the Sun, Fe abundance measurements yield a small line-by-line
scatter (0.08 dex) with a mean abundance of 7.44 dex in good agreement with
recent publications.Comment: Accepted for publication in Mon. Not. R. Astron. So
Current reservoirs in the simple exclusion process
We consider the symmetric simple exclusion process in the interval
with additional birth and death processes respectively on , , and
. The exclusion is speeded up by a factor , births and deaths
by a factor . Assuming propagation of chaos (a property proved in a
companion paper "Truncated correlations in the stirring process with births and
deaths") we prove convergence in the limit to the linear heat
equation with Dirichlet condition on the boundaries; the boundary conditions
however are not known a priori, they are obtained by solving a non linear
equation. The model simulates mass transport with current reservoirs at the
boundaries and the Fourier law is proved to hold
Families of Vicious Walkers
We consider a generalisation of the vicious walker problem in which N random
walkers in R^d are grouped into p families. Using field-theoretic
renormalisation group methods we calculate the asymptotic behaviour of the
probability that no pairs of walkers from different families have met up to
time t. For d>2, this is constant, but for d<2 it decays as a power t^(-alpha),
which we compute to O(epsilon^2) in an expansion in epsilon=2-d. The second
order term depends on the ratios of the diffusivities of the different
families. In two dimensions, we find a logarithmic decay (ln t)^(-alpha'), and
compute alpha' exactly.Comment: 20 pages, 5 figures. v.2: minor additions and correction
The Hitting Times with Taboo for a Random Walk on an Integer Lattice
For a symmetric, homogeneous and irreducible random walk on d-dimensional
integer lattice Z^d, having zero mean and a finite variance of jumps, we study
the passage times (with possible infinite values) determined by the starting
point x, the hitting state y and the taboo state z. We find the probability
that these passages times are finite and analyze the tails of their cumulative
distribution functions. In particular, it turns out that for the random walk on
Z^d, except for a simple (nearest neighbor) random walk on Z, the order of the
tail decrease is specified by dimension d only. In contrast, for a simple
random walk on Z, the asymptotic properties of hitting times with taboo
essentially depend on the mutual location of the points x, y and z. These
problems originated in our recent study of branching random walk on Z^d with a
single source of branching
Electric-dipole active two-magnon excitation in {\textit{ab}} spiral spin phase of a ferroelectric magnet GdTbMnO
A broad continuum-like spin excitation (1--10 meV) with a peak structure
around 2.4 meV has been observed in the ferroelectric spiral spin phase of
GdTbMnO by using terahertz (THz) time-domain spectroscopy.
Based on a complete set of light-polarization measurements, we identify the
spin excitation active for the light vector only along the a-axis, which
grows in intensity with lowering temperature even from above the magnetic
ordering temperature but disappears upon the transition to the -type
antiferromagnetic phase. Such an electric-dipole active spin excitation as
observed at THz frequencies can be ascribed to the two-magnon excitation in
terms of the unique polarization selection rule in a variety of the
magnetically ordered phases.Comment: 11 pages including 3 figure
Quantum Hall Smectics, Sliding Symmetry and the Renormalization Group
In this paper we discuss the implication of the existence of a sliding
symmetry, equivalent to the absence of a shear modulus, on the low-energy
theory of the quantum hall smectic (QHS) state. We show, through
renormalization group calculations, that such a symmetry causes the naive
continuum approximation in the direction perpendicular to the stripes to break
down through infrared divergent contributions originating from naively
irrelevant operators. In particular, we show that the correct fixed point has
the form of an array of sliding Luttinger liquids which is free from
superficially "irrelevant operators". Similar considerations apply to all
theories with sliding symmetries.Comment: 7 pages, 3 figure
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