8,910 research outputs found
Large deviations for intersection local times in critical dimension
Let be a continuous time simple random walk on
(), and let be the time spent by on the site
up to time . We prove a large deviations principle for the -fold
self-intersection local time in the
critical case . When is integer, we obtain similar results
for the intersection local times of independent simple random walks.Comment: Published in at http://dx.doi.org/10.1214/09-AOP499 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A note on random walk in random scenery
We consider a d-dimensional random walk in random scenery X(n), where the
scenery consists of i.i.d. with exponential moments but a tail decay of the
form exp(-c t^a) with a<d/2. We study the probability, when averaged over both
randomness, that {X(n)>ny}. We show that this probability is of order
exp(-(ny)^b) with b=a/(a+1).Comment: 13 page
Quenched large deviations for diffusions in a random Gaussian shear flow drift
We prove a full large deviations principle in large time, for a diffusion
process with random drift V, which is a centered Gaussian shear flow random
field. The large deviations principle is established in a ``quenched'' setting,
i.e. is valid almost surely in the randomness of V.Comment: 29 page
Large deviations for Brownian motion in a random scenery
We prove large deviations principles in large time, for the Brownian
occupation time in random scenery. The random scenery is constant on unit
cubes, and consist of i.i.d. bounded variables, independent of the Brownian
motion. This model is a time-continuous version of Kesten and Spitzer's random
walk in random scenery. We prove large deviations principles in ``quenched''
and ``annealed'' settings.Comment: 29 page
Three-flavor analysis of long-baseline experiments
We compare the analysis of existing and future neutrino oscillation
long-baseline experiments, where we point out that the analysis of future
experiments actually implies a 12-dimensional parameter space. Within the
three-flavor neutrino oscillation framework, six of these parameters are the
fit parameters, and six are the simulated parameters. This high-dimensional
parameter space requires the condensation of information and the definition of
performance indicators for the purpose needed. As the most sophisticated
example for such an indicator, we choose the precision of the leptonic CP
phase, and discuss some of the complications of its computation and
interpretation.Comment: Talk given at the 6th International Workshop on Neutrino Factories &
Superbeams, July 26-Aug 1, 2004, Osaka, Japan. 3 page
Thinplate Splines on the Sphere
In this paper we give explicit closed forms for the semi-reproducing kernels
associated with thinplate spline interpolation on the sphere. Polyharmonic or
thinplate splines for were introduced by Duchon and have become
a widely used tool in myriad applications. The analogues for are the thin plate splines for the sphere. The topic was first
discussed by Wahba in the early 1980's, for the case. Wahba
presented the associated semi-reproducing kernels as infinite series. These
semi-reproducing kernels play a central role in expressions for the solution of
the associated spline interpolation and smoothing problems. The main aims of
the current paper are to give a recurrence for the semi-reproducing kernels,
and also to use the recurrence to obtain explicit closed form expressions for
many of these kernels. The closed form expressions will in many cases be
significantly faster to evaluate than the series expansions. This will enhance
the practicality of using these thinplate splines for the sphere in
computations
One-Step Recurrences for Stationary Random Fields on the Sphere
Recurrences for positive definite functions in terms of the space dimension
have been used in several fields of applications. Such recurrences typically
relate to properties of the system of special functions characterizing the
geometry of the underlying space. In the case of the sphere the (strict) positive definiteness of the zonal function
is determined by the signs of the coefficients in the
expansion of in terms of the Gegenbauer polynomials , with
. Recent results show that classical differentiation and
integration applied to have positive definiteness preserving properties in
this context. However, in these results the space dimension changes in steps of
two. This paper develops operators for zonal functions on the sphere which
preserve (strict) positive definiteness while moving up and down in the ladder
of dimensions by steps of one. These fractional operators are constructed to
act appropriately on the Gegenbauer polynomials
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