45 research outputs found
Impact of survey geometry and super-sample covariance on future photometric galaxy surveys
Photometric galaxy surveys probe the late-time Universe where the density field is highly non-Gaussian. A consequence is the emergence of the super-sample covariance (SSC), a non-Gaussian covariance term that is sensitive to fluctuations on scales larger than the survey window. In this work, we study the impact of the survey geometry on the SSC and, subsequently, on cosmological parameter inference. We devise a fast SSC approximation that accounts for the survey geometry and compare its performance to the common approximation of rescaling the results by the fraction of the sky covered by the survey, fSKY, dubbed âfull-sky approximationâ. To gauge the impact of our new SSC recipe, that we call âpartial-skyâ, we perform Fisher forecasts on the parameters of the (w0,âwa)-CDM model in a 3â
Ăâ
2 point analysis, varying the survey area, the geometry of the mask, and the galaxy distribution inside our redshift bins. The differences in the marginalised forecast errors âwith the full-sky approximation performing poorly for small survey areas but excellently for stage-IV-like areasâ are found to be absorbed by the marginalisation on galaxy bias nuisance parameters. For large survey areas, the unmarginalised errors are underestimated by about 10% for all probes considered. This is a hint that, even for stage-IV-like surveys, the partial-sky method introduced in this work will be necessary if tight priors are applied on these nuisance parameters. We make the partial-sky method public with a new release of the public code PySSC
Correlators for the WignerâSmith time-delay matrix of chaotic cavities
We study the WignerâSmith time-delay matrix Q of a ballistic quantum dot supporting N scattering channels. We compute the v-point correlators of the power traces Tr Qk for arbitrary v>1 at leading order for large N using techniques from the random matrix theory approach to quantum chromodynamics. We conjecture that the cumulants of the Tr QkÊŒs are integer-valued at leading order in N and include a MATHEMATICA code that computes their generating functions recursively
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
We derive some new structural results for the transfer matrix of
square-lattice Potts models with free and cylindrical boundary conditions. In
particular, we obtain explicit closed-form expressions for the dominant (at
large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as
the solution of a special one-dimensional polymer model. We also obtain the
large-q expansion of the bulk and surface (resp. corner) free energies for the
zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47}
(resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <=
m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19
Postscript figures. Also included are Mathematica files data_CYL.m and
data_FREE.m. Many changes from version 1: new material on series expansions
and their analysis, and several proofs of previously conjectured results.
Final version to be published in J. Stat. Phy
Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
We study, using transfer-matrix methods, the partition-function zeros of the
square-lattice q-state Potts antiferromagnet at zero temperature (=
square-lattice chromatic polynomial) for the special boundary conditions that
are obtained from an m x n grid with free boundary conditions by adjoining one
new vertex adjacent to all the sites in the leftmost column and a second new
vertex adjacent to all the sites in the rightmost column. We provide numerical
evidence that the partition-function zeros are becoming dense everywhere in the
complex q-plane outside the limiting curve B_\infty(sq) for this model with
ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the
infinite-volume free energy is perfectly analytic in this region.Comment: 114 pages (LaTeX2e). Includes tex file, three sty files, and 23
Postscript figures. Also included are Mathematica files data_Eq.m,
data_Neq.m,and data_Diff.m. Many changes from version 1, including several
proofs of previously conjectured results. Final version to be published in J.
Stat. Phy
Euclid preparation. TBD. Forecast impact of super-sample covariance on 3x2pt analysis with Euclid
Deviations from Gaussianity in the distribution of the fields probed by
large-scale structure surveys generate additional terms in the data covariance
matrix, increasing the uncertainties in the measurement of the cosmological
parameters. Super-sample covariance (SSC) is among the largest of these
non-Gaussian contributions, with the potential to significantly degrade
constraints on some of the parameters of the cosmological model under study --
especially for weak lensing cosmic shear. We compute and validate the impact of
SSC on the forecast uncertainties on the cosmological parameters for the Euclid
photometric survey, obtained with a Fisher matrix analysis, both considering
the Gaussian covariance alone and adding the SSC term -- computed through the
public code PySSC. The photometric probes are considered in isolation and
combined in the `32pt' analysis. We find the SSC impact to be
non-negligible -- halving the Figure of Merit of the dark energy parameters
(, ) in the 32pt case and substantially increasing the
uncertainties on , and for cosmic shear;
photometric galaxy clustering, on the other hand, is less affected due to the
lower probe response. The relative impact of SSC does not show significant
changes under variations of the redshift binning scheme, while it is smaller
for weak lensing when marginalising over the multiplicative shear bias nuisance
parameters, which also leads to poorer constraints on the cosmological
parameters. Finally, we explore how the use of prior information on the shear
and galaxy bias changes the SSC impact. Improving shear bias priors does not
have a significant impact, while galaxy bias must be calibrated to sub-percent
level to increase the Figure of Merit by the large amount needed to achieve the
value when SSC is not included.Comment: 22 pages, 13 figure
Probabilistic Analysis of a Schröder Walk Generation Algorithm
Using some tools from Combinatorics, Probability Theory, and Singularity analysis, we present a complete asymptotic probabilistic analysis of the cost of a Schröder walk generation algorithm proposed by Penaud et al.([13] ). Such a walk S(:) is made of northeast, southeast and east steps, but each east step is made of two time units (if we consider recording the time t on the abscissa and the moves on the ordinates). The walk starts from the origin at time 0, cannot go under the time axis, and we add the constraint S(2n) = 0. Five different probability distributions will appear in the study: Gaussian, Exponential, Geometric, Rayleigh and a new probability distribution, that we can characterize by its density Laplace Transform and its moments