84,934 research outputs found
How to Couple from the Past Using a Read-Once Source of Randomness
We give a new method for generating perfectly random samples from the
stationary distribution of a Markov chain. The method is related to coupling
from the past (CFTP), but only runs the Markov chain forwards in time, and
never restarts it at previous times in the past. The method is also related to
an idea known as PASTA (Poisson arrivals see time averages) in the operations
research literature. Because the new algorithm can be run using a read-once
stream of randomness, we call it read-once CFTP. The memory and time
requirements of read-once CFTP are on par with the requirements of the usual
form of CFTP, and for a variety of applications the requirements may be
noticeably less. Some perfect sampling algorithms for point processes are based
on an extension of CFTP known as coupling into and from the past; for
completeness, we give a read-once version of coupling into and from the past,
but it remains unpractical. For these point process applications, we give an
alternative coupling method with which read-once CFTP may be efficiently used.Comment: 28 pages, 2 figure
From the discrete to the continuous - towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics.
Cylindrical consistency provides a framework in which discretizations mirror
exactly the continuum limit. Being a standard tool for the kinematics of loop
quantum gravity we propose a coarse graining procedure that aims at
constructing a cylindrically consistent dynamics in the form of transition
amplitudes and Hamilton's principal functions. The coarse graining procedure,
which is motivated by tensor network renormalization methods, provides a
systematic approximation scheme towards this end. A crucial role in this coarse
graining scheme is played by embedding maps that allow the interpretation of
discrete boundary data as continuum configurations. These embedding maps should
be selected according to the dynamics of the system, as a choice of embedding
maps will determine a truncation of the renormalization flow.Comment: 22 page
The Tate conjecture for K3 surfaces in odd characteristic
We show that the classical Kuga-Satake construction gives rise, away from
characteristic 2, to an open immersion from the moduli of primitively polarized
K3 surfaces (of any fixed degree) to a certain regular integral model for a
Shimura variety of orthogonal type. This allows us to attach to every polarized
K3 surface in odd characteristic an abelian variety such that divisors on the
surface can be identified with certain endomorphisms of the attached abelian
variety. In turn, this reduces the Tate conjecture for K3 surfaces over
finitely generated fields of odd characteristic to a version of the Tate
conjecture for certain endomorphisms on the attached Kuga-Satake abelian
variety, which we prove. As a by-product of our methods, we also show that the
moduli stack of primitively polarized K3 surfaces of degree 2d is
quasi-projective and, when d is not divisible by p^2, is geometrically
irreducible in characteristic p. We indicate how the same method applies to
prove the Tate conjecture for co-dimension 2 cycles on cubic fourfolds
Spatial modeling of extreme snow depth
The spatial modeling of extreme snow is important for adequate risk
management in Alpine and high altitude countries. A natural approach to such
modeling is through the theory of max-stable processes, an infinite-dimensional
extension of multivariate extreme value theory. In this paper we describe the
application of such processes in modeling the spatial dependence of extreme
snow depth in Switzerland, based on data for the winters 1966--2008 at 101
stations. The models we propose rely on a climate transformation that allows us
to account for the presence of climate regions and for directional effects,
resulting from synoptic weather patterns. Estimation is performed through
pairwise likelihood inference and the models are compared using penalized
likelihood criteria. The max-stable models provide a much better fit to the
joint behavior of the extremes than do independence or full dependence models.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS464 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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