952 research outputs found
Optimal minimax strategy in a dice game
Each of two players, by turns, rolls a dice several times accumulating the
successive scores until he decides to stop, or he rolls an ace. When stopping,
the accumulated turn score is added to the player account and the dice is given
to his opponent. If he rolls an ace, the dice is given to the opponent without
adding any point. In this paper we formulate this game in the framework of
competitive Markov decision processes (also known as stochastic games), show
that the game has a value, provide an algorithm to compute the optimal minimax
strategy, and present results of this algorithm in three different variants of
the game.Comment: 14 page
MPTbreeze: A fast renormalized perturbative scheme
We put forward and test a simple description of multi-point propagators (MP),
which serve as building-blocks to calculate the nonlinear matter power
spectrum. On large scales these propagators reduce to the well-known kernels in
standard perturbation theory, while at smaller scales they are suppresed due to
nonlinear couplings. Through extensive testing with numerical simulations we
find that this decay is characterized by the same damping scale for both two
and three-point propagators. In turn this transition can be well modeled with
resummation results that exponentiate one-loop computations. For the first
time, we measure the four components of the non-linear (two-point) propagator
using dedicated simulations started from two independent random Gaussian fields
for positions and velocities, verifying in detail the fundamentals of
propagator resummation.
We use these results to develop an implementation of the MP-expansion for the
nonlinear power spectrum that only requires seconds to evaluate at BAO scales.
To test it we construct six suites of large numerical simulations with
different cosmologies. From these and
LasDamas runs we show that the nonlinear power spectrum can be described at
the ~ 2% level at BAO scales for redshifts in the range [0-2.5]. We make a
public release of the MPTbreeze code with the hope that it can be useful to the
community.Comment: 16 pages, 10 figures. Accepted for publication in MNRAS (minor
comments included to match accepted version). Public code available at
http://maia.ice.cat/crocce/mptbreeze
Modeling the angular correlation function and its full covariance in Photometric Galaxy Surveys
Near future cosmology will see the advent of wide area photometric galaxy
surveys, like the Dark Energy Survey (DES), that extent to high redshifts (z ~
1 - 2) but with poor radial distance resolution. In such cases splitting the
data into redshift bins and using the angular correlation function ,
or the power spectrum, will become the standard approach to extract
cosmological information or to study the nature of dark energy through the
Baryon Acoustic Oscillations (BAO) probe. In this work we present a detailed
model for at large scales as a function of redshift and bin width,
including all relevant effects, namely nonlinear gravitational clustering,
bias, redshift space distortions and photo-z uncertainties. We also present a
model for the full covariance matrix characterizing the angular correlation
measurements, that takes into account the same effects as for and
also the possibility of a shot-noise component and partial sky coverage.
Provided with a large volume N-body simulation from the MICE collaboration we
built several ensembles of mock redshift bins with a sky coverage and depth
typical of forthcoming photometric surveys. The model for the angular
correlation and the one for the covariance matrix agree remarkably well with
the mock measurements in all configurations. The prospects for a full shape
analysis of at BAO scales in forthcoming photometric surveys such
as DES are thus very encouraging.Comment: 23 pages, 21 figures Revised version accepted by MNRAS. Description
of mocks re-structured. Mocks including redshift distortions and Photo-z
publicly available at http://www.ice.cat/mic
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